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Vedmedyk [2.9K]
3 years ago
7

What is tan(sin^-1(x/2))

Mathematics
1 answer:
ki77a [65]3 years ago
6 0

Let

\theta=\sin^{-1}\dfrac x2\implies\sin\theta=\dfrac x2

Recall that

\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\dfrac{x^2}4}

Then

\tan\theta=\dfrac{\sin\theta}{\cos\theta}\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac{\frac x2}{\sqrt{1-\frac{x^2}4}}

\implies\tan\left(\sin^{-1}\dfrac x2\right)=\dfrac x{\sqrt{4-x^2}}

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