# Rewrite the expression as an algebraic expression in x. tan(sin^(-1)(x))

Rewrite the expression as an algebraic expression in x.
$\mathrm{tan}\left({\mathrm{sin}}^{-1}\left(x\right)\right)$
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trestegp0
Given:
$\mathrm{tan}\left({\mathrm{sin}}^{-1}\left(x\right)\right)$
Let ${\mathrm{sin}}^{-1}\left(x\right)=\theta \phantom{\rule{0ex}{0ex}}\mathrm{sin}\theta =x$
Therefore,
$\mathrm{cos}\theta =\sqrt{1-{\mathrm{sin}}^{2}\theta }\phantom{\rule{0ex}{0ex}}\mathrm{cos}\theta =\sqrt{1-{x}^{2}}$
Put ${\mathrm{sin}}^{-1}\left(x\right)=\theta$ in equation
$\mathrm{tan}\left({\mathrm{sin}}^{-1}\left(x\right)\right)=\mathrm{tan}\theta \phantom{\rule{0ex}{0ex}}\mathrm{tan}\left({\mathrm{sin}}^{-1}\left(x\right)\right)=\frac{\mathrm{sin}\theta }{\mathrm{cos}\theta }\phantom{\rule{0ex}{0ex}}\mathrm{tan}\left({\mathrm{sin}}^{-1}\left(x\right)\right)=\frac{x}{\sqrt{1-{x}^{2}}}$