Solve the following equations :
cos 4x = cos 2x
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,
If cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.
From above expression and on comparison with standard equation we have:
y = 2x
∴ 4
Hence,
or
∴ or
⇒ x = nπ or
∴ where m, n ϵ Z ..ans