Find the general solutions of the following equations :

sin 3x + cos 2x = 0

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,

We know that: sin θ = cos (π/2 – θ)

∴

⇒

We know that: -cos θ = cos (π – θ)

∴

⇒

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

From above expression and on comparison with standard equation we have:

y =

∴

Hence,

or

∴ or

⇒ or

∴ ,where n ϵ Z