Search any question & find its solution
Question:
Answered & Verified by Expert
If $\alpha=\frac{180^{\circ}}{7}$, then $3 \sin \alpha-4 \sin ^3 \alpha$ is equal to
Options:
Solution:
2897 Upvotes
Verified Answer
The correct answer is:
$\sin 4 \alpha$
Given,
$$
\begin{aligned}
& \alpha=\frac{180^{\circ}}{7} \\
& 3 \sin \alpha-4 \sin ^3 \alpha=\sin 3 \alpha \\
& =\sin (7 \alpha-4 \pi) \\
& =\sin (\pi-4 \alpha) \quad[\because 7 \alpha=\pi] \\
& =\sin 4 \alpha \\
&
\end{aligned}
$$
$$
\begin{aligned}
& \alpha=\frac{180^{\circ}}{7} \\
& 3 \sin \alpha-4 \sin ^3 \alpha=\sin 3 \alpha \\
& =\sin (7 \alpha-4 \pi) \\
& =\sin (\pi-4 \alpha) \quad[\because 7 \alpha=\pi] \\
& =\sin 4 \alpha \\
&
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.