AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\alpha=\frac{180^{\circ}}{7}\), then \(3 \sin \alpha-4 \sin ^3 \alpha\) is equal to
- A \(\cos 4 \alpha\)
- B \(\sin 4 \alpha\)
- C \(\cos 3 \alpha\)
- D 0
Answer & Solution
Correct Answer
(B) \(\sin 4 \alpha\)
Step-by-step Solution
Detailed explanation
Given, \[ \begin{aligned} & \alpha=\frac{180^{\circ}}{7} \\ & 3 \sin \alpha-4 \sin ^3 \alpha=\sin 3 \alpha \\ & =\sin (7 \alpha-4 \pi) \\ & =\sin (\pi-4 \alpha) \quad[\because 7 \alpha=\pi] \\ & =\sin 4 \alpha \\ & \end{aligned} \]
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