First slide

Trigonometric equations

Question

The number of values of sin $x$ satisfying $\sin 5 x = 5 \sin x$ is

Moderate

A

0
B

1
C

2
D

3

Solution

We have $16 \sin^{5} x - 20 \sin^{3} x + 5 \sin x - 5 \sin x$
$\Rightarrow \sin^{3} x (16 \sin^{2} x - 20) = 0 \Rightarrow \sin x = 0,$ only one value

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