Question

Chứng minh đẳng thức sau ( đề dưới cmt)

Answer 1

Answer 2

\(\frac{\left(sin^2x\right)^2-\left(cos^2x\right)^2}{2sinxcosx}\)=\(\frac{\left(sin^2x+cos^2x\right).\left(sin^2x-cos^2x\right)}{2sinxcosx}\)=\(\frac{1.\left(sin^2x-cos^2x\right)}{2sinxcosx}\)=\(\frac{sin^2x-cos^2x}{sin2x}\)=\(\frac{\frac{1-cos2x}{2}-\frac{1+cos2x}{2}}{sin2x}\)=\(\frac{1-1-cos2x-cos2x}{2}.\frac{1}{sin2x}\)=\(\frac{-2cos2x}{2sin2x}=\frac{-cos2x}{sin2x}=-cot2x\left(đpcm\right)\)