The value of sin left(2 sin ^{-1} 0.8right) i | vedclass

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Question

(C) Let $	heta = \sin ^{-1} 0.8$. Then $\sin 	heta = 0.8$.We need to find the value of $\sin(2	heta)$.Using the identity $\sin(2	heta) = 2 \sin

Vedclass · Accepted Answer

$0.96$

Vedclass · Answer

(C) Let $	heta = \sin ^{-1} 0.8$. Then $\sin 	heta = 0.8$.We need to find the value of $\sin(2	heta)$.Using the identity $\sin(2	heta) = 2 \sin 	heta \cos 	heta$,we first find $\cos 	heta$.Since $\cos 	heta = \sqrt{1 - \sin^2 	heta} = \sqrt{1 - (0.8)^2} = \sqrt{1 - 0.64} = \sqrt{0.36} = 0.6$.Now,substitute the values into the identity:$\sin(2	heta) = 2 	imes 0.8 	imes 0.6 = 0.96$.

The value of $\sin \left(2 \sin ^{-1} 0.8\right)$ is equal to

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