Find the general solution of

Question

sin²2x = 1-cos2x

Answer 1

sin²2x = 1-cos2x

Recall the formula

sin²2x =(1-cos2x)/2

(1-cos2x)/2=1-cos2x

1-cos2x=2-2cos2x

cos2x=1

2x=2nπ

x=nπ

Comments

cos2x=1

cos (2x) = cos(0)

The genaral solution of cos(θ) = cos(α) is θ = 2nπ ± α, where n is an integer.

2x = 2nπ ± 0 = 2nπ

⇒ x = nπ.

The general solution of the given equation is x = nπ, where n is an integer.