Question

If $\cos x$, $\cos 2x$, $\cos 3x$ are in A.P. then (where $n\in 1$)-

• A. $x=(2n+1)\frac{\pi }{4}$
• B. $x=n\pi$
• C. $x=(2n+1)\pi$
• D. $x=2n\pi$

Answer 1

The correct option is A $x=(2n+1)\frac{\pi }{4}$

$\cos x,\cos 2x,\cos 3x$ in AP

$2\cos 2x=\cos x+\cos 3x$

$2\cos 2x=2\cos 2x\cos x$

$\cos 2x(1-\cos x)=0$

$\cos 2x.2{\sin }^2\frac{x}{2}=0$

$\cos 2x=0{\sin }^2\frac{x}{2}=0$

$2x=\frac{\pi }{2}(2n+1)\frac{x}{2}=0$ Or $\pi$

$x=\frac{\pi }{4}(2n+1)x=0$ Or $2\pi$

$\therefore x=(2n+1)\frac{\pi }{4}$