Find the general solutions of the following equations :
sin 2x = cos 3x
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,
⇒ {∵ sin θ = cos (π/2 – θ) }
If cos x = cos y then x = 2nπ ± y, where n ∈ Z
Clearly on comparing we have y = 3x
∴
, or
∴ or
Hence,
…ans