If alpha = frac{180^{circ}}{7}, then 3 sin al | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $\alpha = \frac{180^{\circ}}{7}$, which implies $7 \alpha = 180^{\circ} = \pi$.
We know the trigonometric identity $3 \sin \alpha - 4 \sin^{

Vedclass · Accepted Answer

$\sin 4 \alpha$

Vedclass · Answer

(B) Given $\alpha = \frac{180^{\circ}}{7}$, which implies $7 \alpha = 180^{\circ} = \pi$.
We know the trigonometric identity $3 \sin \alpha - 4 \sin^{3} \alpha = \sin 3 \alpha$.
Substituting the expression for $3 \alpha$ using $7 \alpha = \pi$:
$3 \alpha = \pi - 4 \alpha$.
Therefore, $\sin 3 \alpha = \sin(\pi - 4 \alpha)$.
Using the identity $\sin(\pi - 	heta) = \sin 	heta$, we get:
$\sin(\pi - 4 \alpha) = \sin 4 \alpha$.
Thus, $3 \sin \alpha - 4 \sin^{3} \alpha = \sin 4 \alpha$.

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

Similar Questions

If $3 \sin \theta = 2 \sin 3 \theta$ and $0 < \theta < \pi$,then $\sin \theta =$

The value of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $(\sin x)(\cos x) = \frac{1}{4}$ is

The value of $\sin^{2}\left(\frac{\pi}{8}\right) = $

If $x + \frac{1}{x} = 2 \cos \theta,$ then $x^3 + \frac{1}{x^3} = $

The value of $\frac{\cot x - \tan x}{\cot 2x}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module