Question

Решить уравнение: cos4x+sin^22 x=0

Answer 1

Cos4x=1-2sin²2x
1-2sin²2x+sin²2x=0
1-sin²2x=0
sin²2x=1
sin2x=-1⇒2x=-π/2+2πn⇒x=-π/4+πn
sin2x=1⇒2x=π/2+2πn⇒x=π/4+πn