English

CISCE(English Medium) ICSE Class 10

Question Papers

Question Papers409

Textbook Solutions46048

MCQ Online Mock Tests7

Important Solutions6494

Concept Notes & Videos355

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 21 - Trigonometric Identities [Latest edition]

Advertisements

Online Mock Tests

(English Medium) Mathematics1 tests JEE Main Mathematics (JEE Main)8 tests

Chapters

    1: Compound Interest

    2: Sales Tax and Value Added Tax

    3: Banking

    4: Shares and Dividends

    5: Linear Inequations

    6: Quadratic Equations

    7: Problems Based On Quadratic Equations

    8: Reflection

    9: Ratio and Proportion

    10: Remainder And Factor Theorems

    11: Matrices

    12: Distance and Section Formulae

    13: Equation of A Straight Line

    14: Symmetry

    15: Similarity

    16: Loci

    17: Circles

    18: Constructions

    19: Mensuration I

    20: Mensuration II

▶ 21: Trigonometric Identities

    22: Heights and Distances

    23: Graphical Representations

    24: Measures Of Central Tendency

    25: Probability

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 21 - Trigonometric Identities - Shaalaa.com

Advertisements

Solutions for Chapter 21: Trigonometric Identities

Below listed, you can find solutions for Chapter 21 of CISCE Frank for Mathematics - Part 2 [English] Class 10 ICSE.

Exercise 21.1Exercise 21.2Exercise 21.3

Exercise 21.1

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE 21 Trigonometric Identities Exercise 21.1

Exercise 21.1 | Q 1.01

Prove the following identity :

`(1 - sin^2θ)sec^2θ = 1`

Exercise 21.1 | Q 1.02

Prove the following identity :

`(1 - cos^2θ)sec^2θ = tan^2θ`

Exercise 21.1 | Q 1.03

Prove the following identity :

tanA+cotA=secAcosecA

Exercise 21.1 | Q 1.04

Prove the following identity :

`sinθ(1 + tanθ) + cosθ(1 +cotθ) = secθ + cosecθ`

Exercise 21.1 | Q 1.05

Prove the following identity :

( 1 + cotθ - cosecθ) ( 1 + tanθ + secθ)

Exercise 21.1 | Q 1.06

Prove the following identity :

sinθcotθ + sinθcosecθ = 1 + cosθ

Exercise 21.1 | Q 1.07

Prove the following identity :

secA(1 - sinA)(secA + tanA) = 1

Exercise 21.1 | Q 1.08

Prove the following identity :

secA(1 + sinA)(secA - tanA) = 1

Exercise 21.1 | Q 1.09

Prove the following identity :

cosecθ(1 + cosθ)(cosecθ - cotθ) = 1

Exercise 21.1 | Q 1.1

Prove the following identity :

`(secA - 1)/(secA + 1) = (1 - cosA)/(1 + cosA)`

Exercise 21.1 | Q 1.11

Prove the following identity :

`(1 + sinA)/(1 - sinA) = (cosecA + 1)/(cosecA - 1)`

Exercise 21.1 | Q 1.12

Prove the following identity :

`cosA/(1 + sinA) = secA - tanA`

Exercise 21.1 | Q 1.13

Prove the following identity :

`(tanθ + secθ - 1)/(tanθ - secθ + 1) = (1 + sinθ)/(cosθ)`

Exercise 21.1 | Q 2.01

Prove the following identity :

`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`

Exercise 21.1 | Q 2.02

Prove the following identity :

`(1 - tanA)^2 + (1 + tanA)^2 = 2sec^2A`

Exercise 21.1 | Q 2.03

Prove the following identity :

`cosec^4A - cosec^2A = cot^4A + cot^2A`

Exercise 21.1 | Q 2.04

Prove the following identity :

`sec^2A + cosec^2A = sec^2Acosec^2A`

Exercise 21.1 | Q 2.05

Prove the following identity :

`cos^4A - sin^4A = 2cos^2A - 1`

Exercise 21.1 | Q 2.06

Prove the following identity :

`tan^2A - sin^2A = tan^2A.sin^2A`

Exercise 21.1 | Q 2.07

Prove the following identity :

(secA - cosA)(secA + cosA) = `sin^2A + tan^2A`

Exercise 21.1 | Q 2.08

Prove the following identity :

`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`

Exercise 21.1 | Q 2.09

Prove the following identity :

`(cosecA - sinA)(secA - cosA)(tanA + cotA) = 1`

Exercise 21.1 | Q 2.1

Prove the following identity :

`sec^2A.cosec^2A = tan^2A + cot^2A + 2`

Exercise 21.1 | Q 2.11

Prove the following identity :

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`

Exercise 21.1 | Q 2.12

Prove the following identity :

`cosA/(1 - tanA) + sinA/(1 - cotA) = sinA + cosA`

Exercise 21.1 | Q 2.13

Prove the following identity :

`(cosecA - sinA)(secA - cosA) = 1/(tanA + cotA)`

Exercise 21.1 | Q 2.14

Prove the following identity :

`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`

Exercise 21.1 | Q 2.15

Prove the following Identities :

`(cosecA)/(cotA+tanA)=cosA`

Exercise 21.1 | Q 2.16

Prove the following identities:

`(tan"A"+tan"B")/(cot"A"+cot"B")=tan"A"tan"B"`

Exercise 21.1 | Q 2.17

Prove the following identities:

`(sec"A"-1)/(sec"A"+1)=(sin"A"/(1+cos"A"))^2`

Exercise 21.1 | Q 3.01

Prove the following identity :

`sinA/(1 + cosA) + (1 + cosA)/sinA = 2cosecA`

Exercise 21.1 | Q 3.02

Prove the following identity :

`(1 + cosA)/(1 - cosA) = (cosecA + cotA)^2`

Exercise 21.1 | Q 3.03

Prove the following identity :

`(cotA + tanB)/(cotB + tanA) = cotAtanB`

Exercise 21.1 | Q 3.04

Prove the following identity :

`1/(tanA + cotA) = sinAcosA`

Exercise 21.1 | Q 3.05

Prove the following identity :

`tanA - cotA = (1 - 2cos^2A)/(sinAcosA)`

Exercise 21.1 | Q 3.06

Prove the following identity :

`((1 + tan^2A)cotA)/(cosec^2A) = tanA`

Exercise 21.1 | Q 3.07

Prove the following identity :

`cosecA + cotA = 1/(cosecA - cotA)`

Exercise 21.1 | Q 3.08

Prove the following identity :

`(cosecA)/(cosecA - 1) + (cosecA)/(cosecA + 1) = 2sec^2A`

Exercise 21.1 | Q 3.09

Prove the following identity :

`(1 + cosA)/(1 - cosA) = tan^2A/(secA - 1)^2`

Exercise 21.1 | Q 3.1

Prove the following identity :

`(cotA - cosecA)^2 = (1 - cosA)/(1 + cosA)`

Exercise 21.1 | Q 4.01

Prove the following identity :

`sqrt(cosec^2q - 1) = "cosq cosecq"`

Exercise 21.1 | Q 4.02

Prove the following identity :

`sqrt((1 + sinq)/(1 - sinq)) + sqrt((1- sinq)/(1 + sinq))` = 2secq

Exercise 21.1 | Q 4.03

Prove the following identity :

`sqrt((1 - cosA)/(1 + cosA)) = sinA/(1 + cosA)`

Exercise 21.1 | Q 4.04

Prove the following identity :

`sqrt((1 + cosA)/(1 - cosA)) = cosecA + cotA`

Exercise 21.1 | Q 4.05

Prove the following identity :

`sqrt((secq - 1)/(secq + 1)) + sqrt((secq + 1)/(secq - 1))` = 2 cosesq

Exercise 21.1 | Q 5.01

Prove the following identity :

`(secθ - tanθ)^2 = (1 - sinθ)/(1 + sinθ)`

Exercise 21.1 | Q 5.02

Prove the following identity :

`1/(sinA + cosA) + 1/(sinA - cosA) = (2sinA)/(1 - 2cos^2A)`

Exercise 21.1 | Q 5.03

Prove the following identity :

`(sinA + cosA)/(sinA - cosA) + (sinA - cosA)/(sinA + cosA) = 2/(2sin^2A - 1)`

Exercise 21.1 | Q 5.04

Prove the following identity :

`tan^2A - tan^2B = (sin^2A - sin^2B)/(cos^2Acos^2B)`

Exercise 21.1 | Q 5.05

Prove the following identity :

`cosA/(1 - tanA) + sin^2A/(sinA - cosA) = cosA + sinA`

Exercise 21.1 | Q 5.06

Prove the following identity :

`(1 + tan^2A) + (1 + 1/tan^2A) = 1/(sin^2A - sin^4A)`

Exercise 21.1 | Q 5.07

Prove the following identity :

`(cos^3A + sin^3A)/(cosA + sinA) + (cos^3A - sin^3A)/(cosA - sinA) = 2`

Exercise 21.1 | Q 5.08

Prove the following identity :

`(tanθ + 1/cosθ)^2 + (tanθ - 1/cosθ)^2 = 2((1 + sin^2θ)/(1 - sin^2θ))`

Exercise 21.1 | Q 5.09

Prove the following identity :

`(sinA - sinB)/(cosA + cosB) + (cosA - cosB)/(sinA + sinB) = 0`

Exercise 21.1 | Q 5.1

Prove the following identity :

`1/(cosA + sinA - 1) + 2/(cosA + sinA + 1) = cosecA + secA`

Exercise 21.1 | Q 5.11

Prove the following identity :

`(cotA + cosecA - 1)/(cotA - cosecA + 1) = (cosA + 1)/sinA`

Exercise 21.1 | Q 5.12

Prove the following identity :

`(secA - 1)/(secA + 1) = sin^2A/(1 + cosA)^2`

Exercise 21.1 | Q 6.01

Prove the following identity :

`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`

Exercise 21.1 | Q 6.02

Prove the following identity :

`(cosecθ)/(tanθ + cotθ) = cosθ`

Exercise 21.1 | Q 6.03

Prove the following identity :

`(1 + tan^2θ)sinθcosθ = tanθ`

Exercise 21.1 | Q 6.04

Prove the following identity :

`(1 + sinθ)/(cosecθ - cotθ) - (1 - sinθ)/(cosecθ + cotθ) = 2(1 + cotθ)`

Exercise 21.1 | Q 6.05

Prove the following identity :

`(1 + cotA + tanA)(sinA - cosA) = secA/(cosec^2A) - (cosecA)/sec^2A`

Exercise 21.1 | Q 6.06

Prove the following identity :

`2(sin^6θ + cos^6θ) - 3(sin^4θ + cos^4θ) + 1 = 0`

Exercise 21.1 | Q 6.07

Prove the following identity :

`sin^8θ - cos^8θ = (sin^2θ - cos^2θ)(1 - 2sin^2θcos^2θ)`

Exercise 21.1 | Q 6.08

Prove the following identity :

`sec^4A - sec^2A = sin^2A/cos^4A`

Exercise 21.1 | Q 6.09

Prove the following identity :

`tan^2θ/(tan^2θ - 1) + (cosec^2θ)/(sec^2θ - cosec^2θ) = 1/(sin^2θ - cos^2θ)`

Exercise 21.1 | Q 6.1

Prove the following identity :

`(sec^2θ - sin^2θ)/tan^2θ = cosec^2θ - cos^2θ`

Exercise 21.1 | Q 6.11

Prove the following identity :

`(cos^3θ + sin^3θ)/(cosθ + sinθ) + (cos^3θ - sin^3θ)/(cosθ - sinθ) = 2`

Exercise 21.1 | Q 6.12

Prove the following identity :

`(tanθ + sinθ)/(tanθ - sinθ) = (secθ + 1)/(secθ - 1)`

Exercise 21.1 | Q 6.13

Prove the following identity :

`[1/((sec^2θ - cos^2θ)) + 1/((cosec^2θ - sin^2θ))](sin^2θcos^2θ) = (1 - sin^2θcos^2θ)/(2 + sin^2θcos^2θ)`

Exercise 21.1 | Q 6.14

Prove the following identity :

`(cot^2θ(secθ - 1))/((1 + sinθ)) = sec^2θ((1-sinθ)/(1 + secθ))`

Exercise 21.2

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE 21 Trigonometric Identities Exercise 21.2

Exercise 21.2 | Q 1

If m = a secA + b tanA and n = a tanA + b secA , prove that m² - n² = a² - b²

Exercise 21.2 | Q 2

If `x/(a cosθ) = y/(b sinθ) "and" (ax)/cosθ - (by)/sinθ = a^2 - b^2 , "prove that" x^2/a^2 + y^2/b^2 = 1`

Exercise 21.2 | Q 3

If x = r sinA cosB , y = r sinA sinB and z = r cosA , prove that `x^2 + y^2 + z^2 = r^2`

Exercise 21.2 | Q 4

If sinA + cosA = m and secA + cosecA = n , prove that n(m² - 1) = 2m

Exercise 21.2 | Q 5

If x = acosθ , y = bcotθ , prove that `a^2/x^2 - b^2/y^2 = 1.`

Exercise 21.2 | Q 6

If secθ + tanθ = m , secθ - tanθ = n , prove that mn = 1

Exercise 21.2 | Q 7

If x = asecθ + btanθ and y = atanθ + bsecθ , prove that `x^2 - y^2 = a^2 - b^2`

Exercise 21.2 | Q 8

If tanA + sinA = m and tanA - sinA = n , prove that (`m^2 - n^2)^2` = 16mn

Exercise 21.2 | Q 9

If sinA + cosA = `sqrt(2)` , prove that sinAcosA = `1/2`

Exercise 21.2 | Q 10

If `asin^2θ + bcos^2θ = c and p sin^2θ + qcos^2θ = r` , prove that (b - c)(r - p) = (c - a)(q - r)

Exercise 21.3

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE 21 Trigonometric Identities Exercise 21.3

Exercise 21.3 | Q 1.01

Without using trigonometric table , evaluate :

`cosec49°cos41° + (tan31°)/(cot59°)`

Exercise 21.3 | Q 1.02

Without using trigonometric table , evaluate :

`(sin47^circ/cos43^circ)^2 - 4cos^2 45^circ + (cos43^circ/sin47^circ)^2`

Exercise 21.3 | Q 1.03

Without using trigonometric table , evaluate :

`cos90^circ + sin30^circ tan45^circ cos^2 45^circ`

Exercise 21.3 | Q 1.04

Without using trigonometric table , evaluate :

`(sin49^circ/sin41^circ)^2 + (cos41^circ/sin49^circ)^2`

Exercise 21.3 | Q 1.05

Without using trigonometric table , evaluate :

`sin72^circ/cos18^circ - sec32^circ/(cosec58^circ)`

Exercise 21.3 | Q 2.01

Find the value of `θ(0^circ < θ < 90^circ)` if :

`cos 63^circ sec(90^circ - θ) = 1`

Exercise 21.3 | Q 2.02

Find the value of `θ(0^circ < θ < 90^circ)` if :

`tan35^circ cot(90^circ - θ) = 1`

Exercise 21.3 | Q 3.01

Without using trigonometric identity , show that :

`sin42^circ sec48^circ + cos42^circ cosec48^circ = 2`

Exercise 21.3 | Q 3.02

Without using trigonometric identity , show that :

`tan10^circ tan20^circ tan30^circ tan70^circ tan80^circ = 1/sqrt(3)`

Exercise 21.3 | Q 3.03

Without using trigonometric identity , show that :

`sin(50^circ + θ) - cos(40^circ - θ) = 0`

Exercise 21.3 | Q 3.04

Without using trigonometric identity , show that :

`cos^2 25^circ + cos^2 65^circ = 1`

Exercise 21.3 | Q 3.05

Without using trigonometric identity , show that :

`sec70^circ sin20^circ - cos20^circ cosec70^circ = 0`

Exercise 21.3 | Q 4

Prove that `sinA/sin(90^circ - A) + cosA/cos(90^circ - A) = sec(90^circ - A) cosec(90^circ - A)`

Exercise 21.3 | Q 5.01

For ΔABC , prove that :

`tan ((B + C)/2) = cot "A/2`

Exercise 21.3 | Q 5.02

For ΔABC , prove that :

`sin((A + B)/2) = cos"C/2`

Exercise 21.3 | Q 6

Prove that `sin(90^circ - A).cos(90^circ - A) = tanA/(1 + tan^2A)`

Exercise 21.3 | Q 7

Find the value of x , if `cosx = cos60^circ cos30^circ - sin60^circ sin30^circ`

Exercise 21.3 | Q 8

Find x , if `cos(2x - 6) = cos^2 30^circ - cos^2 60^circ`

Exercise 21.3 | Q 9

Given `cos38^circ sec(90^circ - 2A) = 1` , Find the value of <A

Exercise 21.3 | Q 10

prove that `1/(1 + cos(90^circ - A)) + 1/(1 - cos(90^circ - A)) = 2cosec^2(90^circ - A)`

Solutions for 21: Trigonometric Identities

Exercise 21.1Exercise 21.2Exercise 21.3

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 21 - Trigonometric Identities - Shaalaa.com

Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 21 - Trigonometric Identities

Shaalaa.com has the CISCE Mathematics Mathematics - Part 2 [English] Class 10 ICSE CISCE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. Frank solutions for Mathematics Mathematics - Part 2 [English] Class 10 ICSE CISCE 21 (Trigonometric Identities) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. Frank textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics - Part 2 [English] Class 10 ICSE chapter 21 Trigonometric Identities are Trigonometric Ratios of Complementary Angles, Trigonometric Identities, Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables, Trigonometry.

Using Frank Mathematics - Part 2 [English] Class 10 ICSE solutions Trigonometric Identities exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in Frank Solutions are essential questions that can be asked in the final exam. Maximum CISCE Mathematics - Part 2 [English] Class 10 ICSE students prefer Frank Textbook Solutions to score more in exams.

Get the free view of Chapter 21, Trigonometric Identities Mathematics - Part 2 [English] Class 10 ICSE additional questions for Mathematics Mathematics - Part 2 [English] Class 10 ICSE CISCE, and you can use Shaalaa.com to keep it handy for your exam preparation.

Notifications

English हिंदी मराठी

Login

Create free account

Course

(English Medium) ICSE Class 10 CISCE

Change mode
Log out