Question

Number of solutions of $\tan x=\sin x$, where $x\in [-3\pi ,3\pi ]$

• A. No solution
• B. 3
• C. Infinitely many
• D. 7

Answer 1

The correct option is D 7

Given: $\tan x=\sin x$
Solutions of equation $\tan x=\sin x$ are same as the number of points of intersections of graphs of $y=\tan x\text{and}y=\sin x$
The graph is given below

it is obvious from the graph that $\tan x=\sin x$ where $\tan x=\sin x=0$
And we know $\tan x=0\iff x=n\pi ,\forall n\in Z$
In the interval $[-3\pi ,3\pi ]$, required solutions are
$x=-3\pi ,-2\pi ,-\pi ,0,\pi ,2\pi ,3\pi$
Hence number of solutions is 7.