Question

giải pt : cos9x + sin10x = cosx

 

Answer 1

\(\Leftrightarrow cos9x-cosx+sin10x=0\)

\(\Leftrightarrow-2sin5x.sin4x+2sin5x.cos5x=0\)

\(\Leftrightarrow sin5x\left(cos5x-sin4x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}sin5x=0\\cos5x=sin4x\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}sin5x=0\\cos5x=cos\left(\dfrac{\pi}{2}-4x\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}5x=k\pi\\5x=\dfrac{\pi}{2}-4x+k2\pi\\5x=4x-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{k\pi}{5}\\x=\dfrac{\pi}{18}+k2\pi.9\\x=-\dfrac{\pi}{2}+k2\pi\end{matrix}\right.\)