Question

Cos^4x-sin^4x=1/2 допоможіть

Answer 1

cos⁴x-sin⁴x=1/2
(cos²x)²-(sin²x)²=1/2
(cos²x-sin²x)*(cos²x+sin²x)=1/2
(cos²x-sin²x)*1=1/2
cos2x=1/2
$2x=-+arccos frac{1}{2}+2 pi n, n$∈Z
$2x=-+ frac{ pi }{3}+2 pi n, n$∈Z
$x=-+ frac{ pi }{6}+ pi n, n$∈Z