Question

gpt

a) \(cos5x.cosx=cos4x\)

b) \(\frac{cosx\left(cosx+2sinx\right)+3sinx\left(sinx+\sqrt{2}\right)}{sin2x-1}=1\)

Answer 1

a.

\(\Leftrightarrow\frac{1}{2}cos6x+\frac{1}{2}cos4x=cos4x\)

\(\Leftrightarrow cos6x=cos4x\)

\(\Leftrightarrow...\)

b.

ĐKXĐ: \(sin2x\ne1\)

\(\Leftrightarrow cos^2x+2sinx.cosx+3sin^2x+3\sqrt{2}sinx=sin2x-1\)

\(\Leftrightarrow1-sin^2x+sin2x+3sin^2x+3\sqrt{2}sinx=sin2x-1\)

\(\Leftrightarrow2sin^2x+3\sqrt{2}sinx+2=0\)

\(\Rightarrow\left[{}\begin{matrix}sinx=-\sqrt{2}\left(l\right)\\sinx=-\frac{\sqrt{2}}{2}\end{matrix}\right.\)