Question

The general values of x for which $\cos 2x,\frac{1}{2}$ and $\sin 2x$ are in AP, are given by

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$1=\cos 2x+\sin 2x$
$\Rightarrow \sin (2x+\frac{\pi }{4})=\frac{1}{\sqrt{2}}$
$2x+\frac{\pi }{4}=n\pi +(-1{)}^n\frac{\pi }{4}$
$\Rightarrow x=n\pi ,n\pi +\frac{\pi }{4}$