If sin 6 theta = 32 cos^5 theta sin theta - 3 | vedclass

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

Question

(D) We know that $\sin 6 	heta = \sin 3(2 	heta)$.Using the identity $\sin 3A = 3 \sin A - 4 \sin^3 A$,we get:$\sin 6 	heta = 3 \sin 2 	heta - 4 \

Vedclass · Accepted Answer

$\sin 2 	heta$

Vedclass · Answer

(D) We know that $\sin 6 	heta = \sin 3(2 	heta)$.Using the identity $\sin 3A = 3 \sin A - 4 \sin^3 A$,we get:$\sin 6 	heta = 3 \sin 2 	heta - 4 \sin^3 2 	heta$.Substitute $\sin 2 	heta = 2 \sin 	heta \cos 	heta$:$\sin 6 	heta = 3(2 \sin 	heta \cos 	heta) - 4(2 \sin 	heta \cos 	heta)^3$$= 6 \sin 	heta \cos 	heta - 4(8 \sin^3 	heta \cos^3 	heta)$$= 6 \sin 	heta \cos 	heta - 32 \sin^3 	heta \cos^3 	heta$$= 6 \sin 	heta \cos 	heta - 32 \sin 	heta \cos^3 	heta (1 - \cos^2 	heta)$$= 6 \sin 	heta \cos 	heta - 32 \sin 	heta \cos^3 	heta + 32 \sin 	heta \cos^5 	heta$$= 32 \cos^5 	heta \sin 	heta - 32 \cos^3 	heta \sin 	heta + 3(2 \sin 	heta \cos 	heta)$$= 32 \cos^5 	heta \sin 	heta - 32 \cos^3 	heta \sin 	heta + 3 \sin 2 	heta$.Comparing this with the given equation $\sin 6 	heta = 32 \cos^5 	heta \sin 	heta - 32 \cos^3 	heta \sin 	heta + 3x$,we find $3x = 3 \sin 2 	heta$,which implies $x = \sin 2 	heta$.

If $\sin 6 \theta = 32 \cos^5 \theta \sin \theta - 32 \cos^3 \theta \sin \theta + 3x$,then $x$ is equal to:

Similar Questions

If $\tan \theta + \tan \left(\theta + \frac{\pi}{3}\right) + \tan \left(\theta + \frac{2\pi}{3}\right) = 3$,then which of the following is equal to $1$?

If $\cos \theta = \frac{-3}{5}$ and $\theta$ does not lie in the second quadrant,then $\tan \frac{\theta}{2} = $

$\tan 20^\circ \tan 40^\circ \tan 60^\circ \tan 80^\circ = $

If $p = \tan 20^{\circ}$,then the value of $\frac{\tan 160^{\circ} - \tan 110^{\circ}}{1 + \tan 160^{\circ} \tan 110^{\circ}}$ in terms of $p$ is

Find the value of $\tan \frac{\pi}{8}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module