English

Prove that: 3 cosec2 60°  - 2 cot2 30°  + sec2 45°  = 0 - Mathematics

Advertisements
Advertisements

Question

Prove that:

3 cosec2 60°  - 2 cot2 30°  + sec2 45°  = 0

Sum

Solution

LHS =3 cosec260° – 2 cot230° + sec245°

=`3(2/sqrt3)^2 – 2(sqrt3)^2 + (sqrt2)^2`

= `3xx4/3-2xx3+2`

= 4 – 6 + 2

= 0

= RHS

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios] - Exercise 23 (A) [Page 291]

APPEARS IN

Selina Concise Mathematics [English] Class 9 ICSE
Chapter 23 Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
Exercise 23 (A) | Q 3.6 | Page 291

RELATED QUESTIONS

If x = 30°, verify that

(i) `\tan 2x=\frac{2\tan x}{1-\tan ^{2}x`

(ii) `\sin x=\sqrt{\frac{1-\cos 2x}{2}}`


An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.


Using the formula, sin(A – B) = sinA cosB – cosA sinB, find the value of sin 15º


If tan (A + B) = `sqrt3` and tan (A – B) = `1/sqrt3`; 0° < A + B ≤ 90°; A > B, find A and B.


`(2 tan 30°)/(1+tan^2 30°)` = ______.


State whether the following is true or false. Justify your answer.

sin (A + B) = sin A + sin B


Evaluate the following :

`(sin 21^@)/(cos 69^@)`


Evaluate the following :

`(sec 70^@)/(cosec 20^@) + (sin 59^@)/(cos 31^@)`


Evaluate the following :

(sin 72° + cos 18°) (sin 72° − cos 18°)


Express each one of the following in terms of trigonometric ratios of angles lying between
0° and 45°

Sin 59° + cos 56°


Prove the following

`(tan (90 - A) cot A)/(cosec^2 A)   - cos^2 A =0`


Prove the following

 sin (50° − θ) − cos (40° − θ) + tan 1° tan 10° tan 20° tan 70° tan 80° tan 89° = 1


Express each of the following in terms of trigonometric ratios of angles lying between 0° and 45°.

sec78° + cosec56°


Prove that:

cos 30° . cos 60° - sin 30° . sin 60°  = 0


secθ . Cot θ= cosecθ ; write true or false


For any angle θ, state the value of: sin2 θ + cos2 θ


If A = 30°;
show that:
cos 2A = cos4 A - sin4 A


Without using tables, evaluate the following: tan230° + tan260° + tan245°


Without using tables, evaluate the following: cosec330° cos60° tan345° sin290° sec245° cot30°.


Without using tables, evaluate the following: 4(sin430° + cos460°) - 3(cos245° - sin290°).


Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°


If A = 30° and B = 60°, verify that: sin (A + B) = sin A cos B + cos A sin B


If A = 30° and B = 60°, verify that: `(sin("A" + "B"))/(cos"A" . cos"B")` = tanA + tanB


Verify the following equalities:

sin2 60° + cos2 60° = 1


Find the value of the following:

(sin 90° + cos 60° + cos 45°) × (sin 30° + cos 0° – cos 45°)


If sin(A + B) = 1 and cos(A – B)= `sqrt(3)/2`, 0° < A + B ≤ 90° and A > B, then find the measures of angles A and B.


`(2/3 sin 0^circ - 4/5 cos 0^circ)` is equal to ______.


Find the value of x if `2 "cosec"^2 30 + x sin^2 60 - 3/4 tan^2 30` = 10


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×