Question

√2cos^3x-√2cosx+sin^2x=0

Answer 1

$sqrt{2}cos^{3}(x)-sqrt{2}cos(x)+sin^{2}(x)=0;\ sqrt{2}cos(x)(cos^{2}(x) - 1) + sin^{2}(x) = 0;\ -sqrt{2}cos(x)sin^{2}(x) + sin^{2}(x) = 0;\ sin^{2}(x)(1 - sqrt{2}cos(x)) = 0;\ left[begin{array}{c} sin(x) = 0\cos(x) = frac{sqrt{2}}{2}end{array}right$
$left[begin{array}{c} x = left[begin{array}{c} arcsin(0) + 2pi k\pi - arcsin(0) +2pi n end{array}right\ \x = left[begin{array}{c} arccos( frac{sqrt{2}}{2}) + 2pi m\-arccos(frac{sqrt{2}}{2}) + 2pi l end{array}right end{array}right k,n,l,m in mathbb Z$

Ответ:
$left[begin{array}{c} x = left[begin{array}{c} 2pi k\pi +2pi n end{array}right\ \x = left[begin{array}{c} frac{pi}{4} + 2pi m\-frac{pi}{4} + 2pi l end{array}right end{array}right k,n,l,m in mathbb Z$