Question

Answer 1

Ta có: \(\sin5x-2\cdot\sin x\cdot\left(cos2x+cos4x\right)=\sin x\)

=>\(\sin5x-\sin x-2\cdot\sin x\cdot\left(\cos2x+cos4x\right)=0\)

=>\(2\cdot cos\left(\frac{5x+x}{2}\right)\cdot\sin\left(\frac{5x-x}{2}\right)-2\cdot\sin x\cdot2\cdot cos\left(\frac{2x+4x}{2}\right)\cdot cos\left(\frac{4x-2x}{2}\right)=0\)

=>\(2\cdot cos3x\cdot\sin2x-4\cdot\sin x\cdot cos3x\cdot cosx=0\)

=>\(4\cdot\sin x\cdot cosx\cdot cos3x-4\cdot\sin x\cdot cos3x\cdot cosx=0\)

=>\(0x=0\) (luôn đúng)

=>x∈R