Solve the following equations :

cos x + sin x = cos 2x + sin 2x

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ⁿy, where n ∈ Z.

• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.

• tan x = tan y, implies x = nπ + y, where n ∈ Z.

Given,

cos x + sin x = cos 2x + sin 2x

cos x – cos 2x = sin 2x – sin x

{∵ sin A - sin B =

∴

⇒ .

∴ .

Hence,

Either,

⇒

If tan x = tan y, implies x = nπ + y, where n ∈ Z.

∴

⇒ where m,n ϵ Z ….ans