sin 4theta can be written as | vedclass

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Question

(A) We know that $\sin 2A = 2\sin A \cos A$. Applying this to $\sin 4	heta$,we get $\sin 4	heta = 2\sin 2	heta \cos 2	heta$. Using the identities

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) We know that $\sin 2A = 2\sin A \cos A$. Applying this to $\sin 4	heta$,we get $\sin 4	heta = 2\sin 2	heta \cos 2	heta$. Using the identities $\sin 2	heta = 2\sin 	heta \cos 	heta$ and $\cos 2	heta = 1 - 2\sin^2 	heta$,we substitute these into the expression: $\sin 4	heta = 2(2\sin 	heta \cos 	heta)(1 - 2\sin^2 	heta)$. Since $\cos 	heta = \sqrt{1 - \sin^2 	heta}$,we substitute this to express the entire equation in terms of $\sin 	heta$: $\sin 4	heta = 4\sin 	heta \sqrt{1 - \sin^2 	heta} (1 - 2\sin^2 	heta)$.

$\sin 4\theta$ can be written as

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