sin 4theta can be written as | vedclass

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Question

(A) We know that $\sin 4	heta = 2\sin 2	heta \cos 2	heta$. Using the double angle formulas $\sin 2	heta = 2\sin 	heta \cos 	heta$ and $\cos 2	h

Vedclass · Accepted Answer

$4\sin 	heta (1 - 2\sin^2 	heta )\sqrt{1 - \sin^2 	heta}$

Vedclass · Answer

(A) We know that $\sin 4	heta = 2\sin 2	heta \cos 2	heta$. Using the double angle formulas $\sin 2	heta = 2\sin 	heta \cos 	heta$ and $\cos 2	heta = 1 - 2\sin^2 	heta$,we get: $\sin 4	heta = 2(2\sin 	heta \cos 	heta)(1 - 2\sin^2 	heta)$. Since $\cos 	heta = \sqrt{1 - \sin^2 	heta}$ (assuming $\cos 	heta > 0$),we can write: $\sin 4	heta = 4\sin 	heta (1 - 2\sin^2 	heta)\sqrt{1 - \sin^2 	heta}$.

$\sin 4\theta$ can be written as

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