Question

If $\sin 2x-4cosx$ , 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. $2n\pi \pm \frac{\pi }{2},n\in Z$

Answer 1

Answer: (D)

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