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

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

Question

(D) We know that $\sin 6	heta = 2\sin 3	heta \cos 3	heta$. Using the identities $\sin 3	heta = 3\sin	heta - 4\sin^3	heta$ and $\cos 3	heta = 4\

Vedclass · Accepted Answer

$\sin 2	heta$

Vedclass · Answer

(D) We know that $\sin 6	heta = 2\sin 3	heta \cos 3	heta$. Using the identities $\sin 3	heta = 3\sin	heta - 4\sin^3	heta$ and $\cos 3	heta = 4\cos^3	heta - 3\cos	heta$: $\sin 6	heta = 2(3\sin	heta - 4\sin^3	heta)(4\cos^3	heta - 3\cos	heta)$ $= 2(12\sin	heta \cos^3	heta - 9\sin	heta \cos	heta - 16\sin^3	heta \cos^3	heta + 12\sin^3	heta \cos	heta)$ $= 24\sin	heta \cos^3	heta - 18\sin	heta \cos	heta - 32\sin^3	heta \cos^3	heta + 24\sin^3	heta \cos	heta$ By rearranging and using $\sin^2	heta = 1 - \cos^2	heta$,we simplify the expression to match the form $32\cos^5	heta \sin	heta - 32\cos^3	heta \sin	heta + 3x$. After algebraic simplification,we find that $3x = 3\sin 2	heta$. Therefore,$x = \sin 2	heta$.

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

Similar Questions

$\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 8 \theta}}} = $

If $\tan x = \frac{3}{4}$ and $\pi < x < \frac{3\pi}{2}$,find the values of $\sin \frac{x}{2}$,$\cos \frac{x}{2}$,and $\tan \frac{x}{2}$.

If $\tan \alpha = \frac{-12}{5}$,$\cot \beta = \frac{7}{24}$,$\alpha$ does not belong to the second quadrant,and $\beta$ does not belong to the first quadrant,then $\sqrt{13} \sin \frac{\alpha}{2} + \cos \frac{\beta}{2} + \tan \frac{\alpha}{2} \cot \frac{\beta}{2} = $

The value of $\cos (\frac{\pi}{5})$ is ...

The value of $\sin 10^{\circ} \cdot \sin 30^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module