For some a, b, c in R,if sin 5 theta = a cos^ | vedclass

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

Question

(D) We know that $\sin 5 	heta = \sin(3 	heta + 2 	heta) = \sin 3 	heta \cos 2 	heta + \cos 3 	heta \sin 2 	heta$. Using the identities $\sin 3

Vedclass · Accepted Answer

-$50$

Vedclass · Answer

(D) We know that $\sin 5 	heta = \sin(3 	heta + 2 	heta) = \sin 3 	heta \cos 2 	heta + \cos 3 	heta \sin 2 	heta$. Using the identities $\sin 3 	heta = 3 \sin 	heta - 4 \sin^3 	heta$,$\cos 2 	heta = 1 - 2 \sin^2 	heta$,$\cos 3 	heta = 4 \cos^3 	heta - 3 \cos 	heta$,and $\sin 2 	heta = 2 \sin 	heta \cos 	heta$: $\sin 5 	heta = (3 \sin 	heta - 4 \sin^3 	heta)(1 - 2 \sin^2 	heta) + (4 \cos^3 	heta - 3 \cos 	heta)(2 \sin 	heta \cos 	heta)$ $= 3 \sin 	heta - 6 \sin^3 	heta - 4 \sin^3 	heta + 8 \sin^5 	heta + 8 \sin 	heta \cos^4 	heta - 6 \sin 	heta \cos^2 	heta$ $= 8 \sin 	heta \cos^4 	heta - 6 \sin 	heta \cos^2 	heta + 10 \sin^3 	heta - 10 \sin^5 	heta + 10 \sin^5 	heta$ Alternatively,expanding $\sin 5 	heta$ in terms of $\sin 	heta$ and $\cos 	heta$: $\sin 5 	heta = 5 \sin 	heta \cos^4 	heta - 10 \sin^3 	heta \cos^2 	heta + \sin^5 	heta$. Comparing this with $a \cos^4 	heta \sin 	heta + b \cos^2 	heta \sin^3 	heta + c \sin^5 	heta$,we get $a = 5$,$b = -10$,and $c = 1$. Therefore,$abc = 5 	imes (-10) 	imes 1 = -50$.

For some $a, b, c \in R$,if $\sin 5 \theta = a \cos^4 \theta \sin \theta + b \cos^2 \theta \sin^3 \theta + c \sin^5 \theta$,then $abc =$

Similar Questions

If $\sin t + \cos t = \frac{1}{5}$,then $\tan \frac{t}{2}$ is equal to:

If $\tan x + \tan \left(x + \frac{\pi}{3}\right) + \tan \left(x + \frac{2\pi}{3}\right) = 3$,then $\tan 3x$ is equal to

If $\cos^3 \theta + \cos^3 \left(\frac{2 \pi}{3} + \theta\right) + \cos^3 \left(\frac{4 \pi}{3} + \theta\right) = \alpha \cos 3 \theta$,then $\alpha$ is equal to

$A$ true statement among the following identities is

Evaluate: $\cos \frac{\pi}{5} \cos \frac{2\pi}{5} \cos \frac{4\pi}{5} \cos \frac{8\pi}{5}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module