thực hiện phép tính

D=\(\tan^620-33\tan^420+27\tan^2-3\)

cho x+y+z+t=2\(\Pi\)

CMR \(\cos^2x+\cos^2y-\cos^2z-\cos^2t=-2\sin\left(x+y\right)\sin\left(y+z\right)\cos\left(x+z\right)\)

CMR

sin3x -2sin³3x+cos2x.sinx=cos5x.sin4x

cho tam giác ABC . CMR

\(tg\frac{A}{2}.tg\frac{B}{2}+tg\frac{B}{2}.tg\frac{C}{2}+tg\frac{C}{2}.tg\frac{A}{2}=1\)

giải pt

\(x^3+3x^2+5x+3=\left(x^2+3\right)\sqrt{x^2+1}\)

cho 3 số thực dương a,b,c

CMR: \(\frac{a^4}{\left(b+c\right)^2}+\frac{b^4}{\left(a+c\right)^2}+\frac{c^4}{\left(a+b\right)^2}\ge\frac{1}{4}\left(a^2+b^2+c^2\right)\)

giải hệ \(\left\{{}\begin{matrix}x^2+y^2+z^2=1\\x^{2012}+y^{2014}+z^{2016}=1\end{matrix}\right.\)

GPT

\(\sqrt{x^2-2x+3}-\sqrt{x^2-6x+11}=\sqrt{3-x}-\sqrt{x-1}\)

giải phương trình

\(\sqrt{x-1}+\sqrt{x^2-1}=\left(x+1\right)\left(3-x\right)\)