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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\sin (x+3 \alpha)+3 \sin (x-\alpha)=0\), then

  1. A \(\tan x=\tan \alpha\)
  2. B \(\tan x=\tan ^2 \alpha\)
  3. C \(\tan x=\tan ^3 \alpha\)
  4. D \(\tan x=3 \tan \alpha\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\tan x=\tan ^3 \alpha\)

Step-by-step Solution

Detailed explanation

\(\sin x \cos 3\alpha + \cos x \sin 3\alpha + 3(\sin x \cos \alpha - \cos x \sin \alpha) = 0\) \(\sin x (\cos 3\alpha + 3\cos \alpha) = \cos x (3\sin \alpha - \sin 3\alpha)\) \(\tan x = \frac{3\sin \alpha - \sin 3\alpha}{\cos 3\alpha + 3\cos \alpha}\)…