Question

sin^2*3x/4 - корень2/2=sinx-cos^2*3x/4+1

Answer 1

$sin^2frac{3x}{4}-frac{sqrt2}{2}=sinx-cos^2 frac{3x}{4}+1\\underbrace {sin^2 frac{3x}{4}+ cos^2frac{3x}{4}}_{1}-frac{sqrt2}{2}-1=sinx\\sinx=-frac{sqrt2}{2}\\x=(-1)^{n}cdot arcsin(-frac{sqrt2}{2})+pi n,; nin Z\\x=(-1)^{n}cdot (-frac{pi}{4})+pi n=(-1)^{n+1}cdot frac{pi}{4}+pi n,; nin Z$