Question

Решить тригонометрическое уравнение
$cos^{2}x + sin^{4}x=1$

Answer 1

$cos^2x+sin^4x=1 \cos^2x+(sin^2x)^2=1 \cos^2x+(1-cos^2x)^2=1 \cos^2x=y \y+(1-y)^2=1 \y^2+y^2-2y+1=1 \2y^2-2y=0 \y^2-y=0 \y(y-1)=0 \y_1=0 \y_2=1 \cos^2x=0 \cosx=0 \x_1= frac{pi}{2} +pi n, n in Z \cos^2x=1 \cosx=pm 1 \cosx=1 \x_2=2pi n, n in Z \cosx=-1 \x_3=pi+2pi n, n in Z$
Ответ: $x_1= frac{pi}{2} +pi n, n in Z; x_2=2pi n, n in Z; x_3=pi+2pi n, n in Z$