If sin 2x = 4 cos x,then x is equal to | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given,$\sin 2x = 4 \cos x$. Using the identity $\sin 2x = 2 \sin x \cos x$,we have: $2 \sin x \cos x = 4 \cos x$ $2 \sin x \cos x - 4 \cos x = 0$

Vedclass · Accepted Answer

$2n \pi \pm \frac{\pi}{2}, n \in Z$

Vedclass · Answer

(D) Given,$\sin 2x = 4 \cos x$. Using the identity $\sin 2x = 2 \sin x \cos x$,we have: $2 \sin x \cos x = 4 \cos x$ $2 \sin x \cos x - 4 \cos x = 0$ $2 \cos x (\sin x - 2) = 0$ This implies either $\cos x = 0$ or $\sin x = 2$. Since the range of $\sin x$ is $[-1, 1]$,$\sin x = 2$ has no real solution. Thus,$\cos x = 0$. The general solution for $\cos x = 0$ is $x = (2n + 1) \frac{\pi}{2}$,which can be written as $x = n \pi + \frac{\pi}{2}$ or $x = 2n \pi \pm \frac{\pi}{2}$ for $n \in Z$.

If $\sin 2x = 4 \cos x$,then $x$ is equal to

Similar Questions

If $\sec x \cos 5x + 1 = 0$,where $0 < x < 2\pi$,then $x =$

The number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = -\frac{1}{2}$ for $\theta \in \left( 0, \frac{\pi}{2} \right)$ is:

The general solution of $\tan 3x = 1$ is

The number of distinct solutions of the equation $\log _{\frac{1}{2}}|\sin x|=2-\log _{\frac{1}{2}}|\cos x|$ in the interval $[0,2 \pi]$ is

The values of $x$ satisfying the equation $3 \operatorname{cosec} x = 4 \sin x$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module