Question

\(2\cos^2\frac{x}{2}\left(1-\sin x\right)+\cos^2x=0\)

Answer 1

\(\Leftrightarrow\left(1+cosx\right)\left(1-sinx\right)+1-sin^2x=0\)

\(\Leftrightarrow\left(1+cosx\right)\left(1-sinx\right)+\left(1-sinx\right)\left(1+sinx\right)=0\)

\(\Leftrightarrow\left(1-sinx\right)\left(cosx+sinx+2\right)=0\)

\(\Leftrightarrow\left(1-sinx\right)\left(\sqrt{2}sin\left(x+\frac{\pi}{4}\right)+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sinx=1\Rightarrow x=?\\sin\left(x+\frac{\pi}{4}\right)=-\sqrt{2}\left(vn\right)\end{matrix}\right.\)