Question

The number of solutions in the interval $[0,\pi ]$ of the equation ${\sin }^{3}x\cos 3x+\sin 3x{\cos }^{3}x=0$ is equal to

• A. 7
• B. 6
• C. 5
• D. 4

Answer 1

Answer: (C)

The number of solutions in the interval $[0,\pi ]$ of the equation
${\sin }^{3}x\cos 3x+\sin 3x{\cos }^{3}x=0$ is
equal toThe given equation can be written as
$\left(\frac{3\sin x-\sin 3x}{4}\right)\cos 3x+\sin 3x\left(\frac{3\cos x+\cos 3x}{4}\right)$
$\sin x\cos 3x+\cos x\sin 3x=0$
So, $\sin (x+3x)=0\Rightarrow \sin 4x=0$
$\Rightarrow x=\frac{n\pi }{4},n\in Z.$
$\Rightarrow x=0,\frac{\pi }{4},\frac{\pi }{2},\frac{3\pi }{4},\pi$
$\Rightarrow 5$solutions