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AP EAMCET · Maths · Trigonometric Ratios & Identities

If \(\alpha=\frac{180^{\circ}}{7}\), then \(3 \sin \alpha-4 \sin ^3 \alpha\) is equal to

  1. A \(\cos 4 \alpha\)
  2. B \(\sin 4 \alpha\)
  3. C \(\cos 3 \alpha\)
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sin 4 \alpha\)

Step-by-step Solution

Detailed explanation

Given, \[ \begin{aligned} & \alpha=\frac{180^{\circ}}{7} \\ & 3 \sin \alpha-4 \sin ^3 \alpha=\sin 3 \alpha \\ & =\sin (7 \alpha-4 \pi) \\ & =\sin (\pi-4 \alpha) \quad[\because 7 \alpha=\pi] \\ & =\sin 4 \alpha \\ & \end{aligned} \]