CMR

\(\frac{cot^2\left(\frac{x}{2}\right)-cot^2\left(\frac{3x}{2}\right)}{cos^2\left(\frac{x}{2}\right).cosx.\left(1+cot^2\frac{3x}{2}\right)}=8\)

CMR

\(\frac{\sqrt{2}cosx-2cos\left(\frac{\pi}{4}+x\right)}{2sin\left(\frac{\pi}{4}+x\right)-\sqrt{2}sinx}=tanx\)

CMR

( tanx-1)/cos4x = (sin 2x-cos 2x)/(sin 2x+cos 2x)

\(\frac{1-2sin^22x}{1-sin4x}=\frac{1+tan2x}{1-tan2x}\)

GPT

a,\(\left\{{}\begin{matrix}x^3=5x+y\\y^3=5y+x\end{matrix}\right.\)

b,\(\left\{{}\begin{matrix}x^2-2y^2=2x+y\\y^2-2x^2=2y+x\end{matrix}\right.\)

\(\left\{{}\begin{matrix}xy\left(x-2\right)=-2\\x^3-y^3=2\end{matrix}\right.\)