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,

We know that sin x, and cos x have positive values in the 1^st and 2^nd quadrant.

While giving solution, we always try to take the least value of y

The first quadrant will give the least magnitude of y.

∴

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

Clearly on comparing we have y = π/3

⇒ ,where n ϵ Z ….ans