Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

Prove that  `2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2`

Prove that  `cot^2  pi/6 + cosec  (5pi)/6 + 3 tan^2  pi/6 = 6`

Prove that: `2 sin^2  (3pi)/4 + 2 cos^2  pi/4  + 2 sec^2  pi/3 = 10`

Find the value of: sin 75°

Find the value of: tan 15°

Prove the following: `cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 -  x)sin (pi/4  - y) =  sin (x + y)`

Prove the following: `(tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2`

Prove the following:

`(cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) =  cot^2 x`

Prove the following:

`cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1`

Prove the following:

`cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x`

Prove the following:

cot 4x (sin 5x + sin 3x) = cot x (sin 5x – sin 3x) 

Prove the following:

`(cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)`

Prove the following:

`(sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x`

Prove the following:

`(sin x -  siny)/(cos x + cos y)= tan  (x -y)/2`

Prove the following:

`(sin x + sin 3x)/(cos x + cos 3x) = tan 2x`

Prove the following:

`(sin x - sin 3x)/(sin^2 x - cos^2 x) =  2sin x`