Решите уравнение 2sin^2x- cos^4x=1-sin^4x

Question

Решите уравнение 2sin^2x- cos^4x=1-sin^4x

Answer 1

= cos^4x - sin^4x
= (cos^2x + sin^2x)(cos^2x - sin^2x)
= (1)(1 - sin^2x - sin^2x)
= 1 - sin^2x - sin^2x
= 1 - 2sin^2x

Answer 2

2sin^2x-cos^4x=1-sin^4x

2sin^2x-cos^4x=cos4x

2sin^2x=0

2x=pin n e Z

x=pi/2n e Z