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

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)`

Prove that: `(cos x  + cos y)^2 + (sin x - sin y )^2 =  4 cos^2  (x + y)/2`

Prove that: `(cos x - cosy)^2 + (sin x - sin y)^2 = 4 sin^2  (x - y)/2`

Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x

Prove that: `((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x`

Prove that: sin 3x + sin 2x – sin x = 4sin x `cos  x/2 cos  (3x)/2`