First slide

Trigonometric equations

Question

Number of values of x lying in the interval $[0, 5 π]$ and satisfying the equation $\sin x = \tan x$ is.

Moderate

A

5
B

6
C

9
D

12

Solution

$\sin x = \tan x \Rightarrow \sin x (\cos x - 1) = 0$
$\Rightarrow \sin x = 0$ or $\cos x = 1$
However when , $\cos x = 1$ , then $\sin x = 0$
$∴ \sin x = 0 \Rightarrow x = 0, π, 2 π, 3 π, 4 π, 5 π$

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