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,

In all such problems we try to reduce the equation in an equation involving single trigonometric expression.

∴

⇒ { ∵ }

⇒ { ∵ sin A cos B + cos A sin B = sin (A +B)}

⇒

NOTE: We can also make the ratio of cos instead of sin, the answer remains same but the form of answer may look different, when you put values of n you will get same values with both forms

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

∴

∴