Question

Total number of solutions that are multiples of $\pi$ of the equation $2x=3\pi (1-\cos x),$is:

• A. 3
• B. 5
• C. 4
• D. 2

Answer 1

The correct option is C 4

$\frac{2x}{3\pi }=1-cosx$

$1-\frac{2x}{3\pi }=cosx$

We know,

$-1\le cosx\le 1$

$-1\le 1-\frac{2x}{3\pi }\le 1$

$0\le \frac{2x}{3\pi }\le 2$

$0\le x\le 3\pi$

since $x$ is a multiple of $\pi$

$x=0,\pi ,2\pi ,3\pi$

so,

it will have $4$ solutions