Question

The number of solution of the equation $\sin 2x-2\cos x-4$ in the interval $[0,5\pi ]$ is

• A. $6$
• B. $4$
• C. $3$
• D. No solution

Answer 1

The correct option is D No solution

$\sin 2x-2\cos x=4$

$2\sin x\cos x-2\cos x=4$

$2\cos x(\sin -1)=4$

$\cos x(\sin x-1)=2$

$[-1,1]$ $[-2,10]$

only solution will be when $\sin x=-1$ & $\cos x=-1$ which us not possible

$\therefore$ no solution