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

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`

Prove the following:

`(cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x`

Prove the following:

`tan 4x = (4tan x(1 - tan^2 x))/(1 - 6tan^2 x + tan^4 x)`