First slide

Trigonometric equations

Question

sin $x,$ sin $2 x, \sin 3 x$ are in A.P. if

Moderate

A

$x = 165 °$
B

$x = 195 °$
C

$x = 15 °$
D

$x = 2 n π n \in I .$

Solution

$\begin{array}{l} \sin x, \sin 2 x, \sin 3 x are in A.P. \\ If 2 \sin 2 x = \sin x + \sin 3 x = 2 \sin 2 x \cos x \\ or if 2 \sin 2 x (1 - \cos x) = 0 \\ or if either \sin 2 x = 0 or \cos x = 1 \\ which is satisfied by x = 2 n π for which \cos x = 1 \end{array}$

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