Selina solutions for Concise Mathematics [English] Class 9 ICSE chapter 22 - Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and their Reciprocals] [Latest edition]

From the following figure, find the values of:

1. sin A
2. cos A
3. cot A
4. sec C
5. cosec C
6. tan C

Form the following figure, find the values of:

1. cos B
2. tan C
3. sin²B + cos²B
4. sin B. cos C + cos B. sin C

From the following figure, find the values of
(i) cos A 
(ii) cosec A
(iii) tan²A - sec²A 
(iv) sin C
(v) sec C 
(vi) cot² C - ` 1 / sin^2 "c"`

From the following figure, find the values of
(i) sin B 
(ii) tan C
(iii) sec² B - tan²B 
(iv) sin²C + cos²C

Given : sin A = `(3)/(5)` , find : (i) tan A (ii) cos A 

From the following figure, find the values of :
(i) sin A
(ii) sec A
(iii) cos² A + sin²A

Given: cos A = `( 5 )/ ( 13 )`

Evaluate:

1. `(sin "A "–cot "A") / (2 tan "A")`
2. `cot "A" + 1/cos"A"`

Given: sec A = `( 29 )/(21), "evaluate : sin A" - 1/tan "A"`

Given: tan A = `4/3 , "find" : ("cosec""A")/(cot "A"– sec "A")`

Given: 4 cot A = 3
find :
(i) sin A
(ii) sec A
(iii) cosec²A - cot²A.

Given: cos A = 0.6; find all other trigonometrical ratios for angle A.

In a right-angled triangle, it is given that A is an acute angle and tan A = `(5) /(12)`.

find the value of :
(i) cos A
(ii) sin A
(iii)  ` (cosA+sinA)/(cosA– sin A)`

Given: sin θ = `p/q`.
Find cos θ + sin θ in terms of p and q.

If cos A = `(1)/(2)` and sin B = `(1)/(sqrt2)`, find the value of: `(tan"A"  –  tan"B")/(1+tan"A" tan"B")`.

Are angles A and B from the same triangle? Explain.

If 5 cot θ = 12, find the value of : Cosec θ+ sec θ 

If tan x = `1(1)/(3)`, find the value of : 4 sin²x - 3 cos²x + 2

If cosec θ = `sqrt5`, find the value of:

1. 2 - sin² θ - cos² θ
2. 2 + `1/sin^2"θ" – cos^2"θ"/sin^2"θ"` 

If sec A = `sqrt2`, find the value of :
`(3cos^2"A"+5tan^2"A")/(4tan^4"A"–sin^2"A")`

If cot θ= 1; find the value of: 5 tan² θ+ 2 sin² θ- 3

In the following figure: 

AD ⊥ BC, AC = 26 CD = 10, BC = 42, ∠DAC = x and ∠B = y.

Find the value of :

(i) cot x

(ii) `1/sin^2 y – 1/tan^2 y`

(iii) `6/cos x – 5/cos y + 8 tan y`.

From the following figure, find:
(i) y
(ii) sin x°
(iii) (sec x° - tan x°) (sec x° + tan x°)

Use the given figure to find :
(i) sin x^o 
(ii) cos y^o
(iii) 3 tan x^o - 2 sin y^o + 4 cos y^o.

In the diagram, given below, triangle ABC is right-angled at B and BD is perpendicular to AC.
Find:

(i) cos ∠DBC

(ii) cot ∠DBA

In the given figure, triangle ABC is right-angled at B. D is the foot of the perpendicular from B to AC. Given that BC = 3 cm and AB = 4 cm.

find :

1. tan ∠DBC
2. sin ∠DBA

In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ∠ABC.

In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:
(i) sin B 
(ii) tan C
(iii) sin² B + cos²B 
(iv) tan C - cot B

In triangle ABC; ∠ABC = 90°, ∠CAB = x°, tan x° = `(3)/(4)` and BC = 15 cm. Find the measures of AB and AC.

Using the measurements given in the following figure:
(i) Find the value of sin θ and tan θ.
(ii) Write an expression for AD in terms of θ

In the given figure;

BC = 15 cm and sin B = `(4)/(5)`

1. Calculate the measure of AB and AC.
2. Now, if tan ∠ADC = 1; calculate the measures of CD and AD.

Also, show that: tan²B - `1/cos^2 "B" = – 1 .`

If sin A + cosec A = 2;

Find the value of sin² A + cosec² A.

If tan A + cot A = 5;
Find the value of tan² A + cot² A.

Given: 4 sin θ = 3 cos θ ; find the value of:
(i) sin θ (ii) cos θ
(iii) cot² θ - cosec² θ .
(iv) 4 cos²θ- 3 sin²θ+2

Given : 17 cos θ = 15;
Find the value of: tan θ + 2 secθ .

Given : 5 cos A - 12 sin A = 0; evaluate:

`(sin "A"+cos"A")/(2 cos"A"– sin"A")`

In the given figure; ∠C = 90^o and D is mid-point of AC.
Find : 
(i) `(tan∠CAB)/ (tan∠CDB)` (ii) `(tan∠ABC)/ (tan∠DBC)`

If 3 cos A = 4 sin A, find the value of :
(i) cos A(ii) 3 - cot² A + cosec²A.

In triangle ABC, ∠B = 90° and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.

In rhombus ABCD, diagonals AC and BD intersect each other at point O.
If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the side and the diagonals of the rhombus.

In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:

1. cos B
2. sin C
3. tan² B - sec² B + 2

In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C = 1.
Find the length of AB, AD, AC, and DC.

Given q tan A = p, find the value of:

`("p" sin "A"  –  "q" cos "A")/("p" sin "A" + "q" cos "A")`.

If sin A = cos A, find the value of 2 tan²A - 2 sec² A + 5.

In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD. 

If 2 sin x = `sqrt3` , evaluate.
(i) 4 sin³ x - 3 sin x.
(ii) 3 cos x - 4 cos³ x.

If sin A = `(sqrt3)/(2)` and cos B = `(sqrt3)/(2)` , find the value of : `(tan"A" – tan"B")/(1+tan"A" tan"B")`

Use the information given in the following figure to evaluate:

`(10)/sin x + (6)/sin y  –  6 cot y`.

If sec A = `sqrt2` , find : `(3cot^2 "A"+ 2 sin^2 "A")/ (tan^2 "A" – cos ^2 "A")`.

If 5 cos θ = 3, evaluate : `(co secθ – cot θ)/(co secθ + cot θ)`

If cosec A + sin A = 5`(1)/(5)`, find the value of cosec²A + sin²A.

If 5 cos  = 6 sin ; evaluate:
(i) tan θ
(ii) `(12 sin θ – 3 cos θ)/(12 sin θ + 3 cos θ)`