Question

\(\frac{\sin^22x-2}{\sin^22x-4\cos^2x}=\tan^2x\)

Answer 1

ĐKXĐ: \(cosx\ne0\)

\(\frac{sin^22x-2}{4sin^2x.cos^2x-4cos^2x}=\frac{sin^2x}{cos^2x}\)

\(\Leftrightarrow\frac{sin^22x-2}{4cos^2x\left(sin^2x-1\right)}=\frac{sin^2x}{cos^2x}\)

\(\Leftrightarrow\frac{2-sin^22x}{4cos^4x}=\frac{sin^2x}{cos^2x}\)

\(\Leftrightarrow2-sin^22x=4sin^2x.cos^2x\)

\(\Leftrightarrow2-sin^22x=sin^22x\)

\(\Leftrightarrow sin^22x=1\Leftrightarrow cos2x=0\)

\(\Rightarrow x=\frac{\pi}{4}+\frac{k\pi}{2}\)