# Please, rewrite the expression as an algebraic expression in x. sin(tan^

Please, rewrite the expression as an algebraic expression in x.
$$\sin(\tan^−1x)$$

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sweererlirumeX

Let $$\displaystyleθ={{\tan}^{{-{{1}}}}{\left({x}\right)}}$$, then $$\tan θ = x$$
Draw a right triangle with $$\displaystyleθ$$ as one of it’s acute angles:
1) $$\displaystyle{A}{C}=\sqrt{{{A}{B}^{{2}}+{D}{C}^{{2}}}}$$
$$\displaystyle{A}{C}=\sqrt{{{x}^{{2}}+{1}^{{2}}}}=\sqrt{{{1}+{x}^{{2}}}}$$
2) $$\displaystyle{\sin{{\left({{\tan}^{{-{{1}}}}{\left({x}\right)}}\right)}}}=\frac{{x}}{{\sqrt{{{1}+{x}^{{2}}}}}}$$