Đáp án:
${\left[\begin{aligned}x=\dfrac{k\pi}{7}\\x=\dfrac{k\pi}{3}\end{aligned}\right.}\\$
Giải thích các bước giải:
$\cos^22x+\sin^25x=1\\
\Leftrightarrow \cos^22x+\sin^25x=\sin^22x+\cos^22x\\
\Leftrightarrow \cos^22x+\sin^25x-\sin^22x-\cos^22x=0\\
\Leftrightarrow \sin^25x-\sin^22x=0\\
\Leftrightarrow (\sin5x-\sin2x)(\sin5x+\sin2x)=0\\
\Leftrightarrow 2\cos\dfrac{5x+2x}{2}\sin\dfrac{5x-2x}{2}.2\sin\dfrac{5x+2x}{2}\cos\dfrac{5x-2x}{2}=0\\
\Leftrightarrow 4\cos\dfrac{7x}{2}\sin\dfrac{3x}{2}\sin\dfrac{7x}{2}\cos\dfrac{3x}{2}=0\\
\Leftrightarrow 2\cos\dfrac{7x}{2}.\sin\dfrac{7x}{2}.2\sin\dfrac{3x}{2}\cos\dfrac{3x}{2}=0\\
\Leftrightarrow \sin7x\sin3x=0\\
\Leftrightarrow {\left[\begin{aligned}\sin7x=0\\\sin3x=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}7x=k\pi\\3x=k\pi\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\dfrac{k\pi}{7}\\x=\dfrac{k\pi}{3}\end{aligned}\right.}\\$
