Solve the following equations :

Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ⁿ y, 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,

⇒

⇒

⇒

∴ tan x = -1 or tan x = √3

As, tan x ϵ (-∞ , ∞) so both values are valid and acceptable.

⇒ tan x = tan (-π/4) or tan x = tan (π/3)

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

Clearly by comparing standard form with obtained equation we have

y = -π/4 or y = π/3

∴ or

Hence,

,where m,n ϵ Z