Mathematics, 16.09.2019 14:30 vixxs345
Write the trigonometric expression tan(sin^-1x) as an algebraic expression in terms of x.
Answers: 1
![\mathsf{sin\,\theta=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\theta=x\qquad\quad(i)}](/tpl/images/0233/2805/a6ae2.png)
then 
is positive. So take the positive square root and you get
![\mathsf{tan\,\theta=\dfrac{sin\,\theta}{cos\,\theta}}\\\\\\ \mathsf{tan\,\theta=\dfrac{x}{\sqrt{1-x^2}}}\\\\\\\\ \therefore~~\mathsf{tan\!\left[sin^{-1}(x)\right]=\dfrac{x}{\sqrt{1-x^2}}\qquad\qquad -1\ \textless \ x\ \textless \ 1.}](/tpl/images/0233/2805/24b97.png)
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Write the trigonometric expression tan(sin^-1x) as an algebraic expression in terms of x....
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