Question

Решите уравнение: 2sin^2 (x) - cos (2x) = 1.

Answer 1

$2sin^2 x - cos 2x = 1$
$2sin^2 x = 1+cos2x$
$2sin^2 x = 2cos^2x$
$sin^2 x = cos^2x$
$sin^2 x -cos^2x=0$
$-(cos^2x-sin^2x)=0$
$cos2x=0$
$2x= frac{ pi }{2} + pi n,$ $n$ ∈ $Z$
$x= frac{ pi }{4} + frac{pi n}{2} ,$ $n$ ∈ $Z$