Question

Giải pt lượng giác Giúp em với em cảm ơn ạ

Answer 1

8.

\(cosx-2sin^2\dfrac{x}{2}=0\)

\(\Leftrightarrow cosx+1-2sin^2\dfrac{x}{2}-1=0\)

\(\Leftrightarrow2cosx-1=0\)

\(\Leftrightarrow cosx=\dfrac{1}{2}\)

\(\Leftrightarrow x=\pm\dfrac{\pi}{3}+k2\pi\)

Answer 2

9.

\(cos^4x-sin^4x=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow\left(cos^2x+sin^2x\right)\left(cos^2x-sin^2x\right)=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow cos2x=\dfrac{\sqrt{2}}{2}\)

\(\Leftrightarrow2x=\pm\dfrac{\pi}{4}+k2\pi\)

\(\Leftrightarrow x=\pm\dfrac{\pi}{8}+k\pi\)