Question

Total number of solution of $sinx.tan4x=cosx$ belonging to (0, $\pi$) are

• A. 4
• B. 7
• C. 8
• D. 5

Answer 1

The correct option is D 5

$\sin x\tan 4x=\cos x$
$\sin x\sin 4x=\cos x\cos 4x$
$\sin x\sin 4x-\cos x\cos 4x=0$
$\cos (x+4x)=0$
$\cos 5x=0$
$5x=\frac{\pi }{2}+k\pi$
$x=\frac{\pi }{10}+k\frac{\pi }{5}$
Thus, $0<\frac{\pi }{10}+k\frac{\pi }{5}<\pi$
$-\frac{1}{2}<k<\frac{9}{2}$
Thus, k = 0, 1,2,3,4
Hence, it has 5 solutions.