Question

Answer 1

\(cos3x+sin3x=4cos^3x-3cosx+3sinx-4sin^3x\\ =4\left(cosx-sinx\right)\left(1+sinxcosx\right)-3\left(cosx-sinx\right)\\ =\left(cosx-sinx\right)\left(1+4sinxcosx\right)\)

pt thành: 

\(5sinx+5cosx-5sinx=cos2x+3\\ \Leftrightarrow2cos^2x-5cosx+2=0\\ \Leftrightarrow cosx=\dfrac{1}{2}\Leftrightarrow x=\pm\dfrac{\pi}{3}+k2\pi,k\in Z\)

+xét \(0< \dfrac{\pi}{3}+k2\pi< 2\pi\\ \Leftrightarrow-\dfrac{1}{6}< k< \dfrac{5}{6}\Leftrightarrow k=0\Rightarrow x=\dfrac{\pi}{3}\)

+xet \(0< -\dfrac{\pi}{3}+k2\pi< 2\pi\Leftrightarrow\dfrac{1}{6}< k< \dfrac{7}{6}\Leftrightarrow k=1\\ \Rightarrow x=\dfrac{5\pi}{3}\)

vay..