Question

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

• A. $\frac{n \pi}{2} \pm \frac{\pi}{4}, n \in Z$
• B. no value
• C. $n \pi +(-1)^n \frac {\pi}{4} n \in Z$
• D. $2 n \pi \pm \frac{\pi}{2}, n \,\in\, Z$

Answer 1

Answer: (D)

Given, sin $2x = 4 \,cos\, x$
$\Rightarrow \, 2 \,sin \,x \,cos \,x = 4 \,cos\, x $
$\Rightarrow \, 2\, cos\, x (sin x - 2) = 0$
$\Rightarrow \, sin \,x = 2$, which is not possible because the value of sin x lies between - 1 and 1.
$\therefore cos \,x = 0$
$\Rightarrow x=2n\,\pi \,\pm \frac{\pi}{2}$