Question

Tìm nghiệm của pt

\(sin^4x-cos^4x-1=2sinx-cos2x\)

Answer 1

\(\Leftrightarrow\left(sin^2x-cos^2x\right)\left(sin^2x+cos^2x\right)-1=2sinx-cos2x\)

\(\Leftrightarrow sin^2x-cos^2x-1=2sinx-cos2x\)

\(\Leftrightarrow-\left(cos^2x-sin^2x\right)-1=2sinx-cos2x\)

\(\Leftrightarrow-cos2x-1=2sinx-cos2x\)

\(\Leftrightarrow2sinx=-1\)

\(\Rightarrow sinx=-\frac{1}{2}=sin\left(-\frac{\pi}{6}\right)\)

\(\Rightarrow\left[{}\begin{matrix}x=-\frac{\pi}{6}+k2\pi\\x=\frac{7\pi}{6}+k2\pi\end{matrix}\right.\)