What is the value of $tan ({sin}^{- 1} x)$ $tan (sin^-1 x)$ ?

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What is the value of $tan ({sin}^{- 1} x)$ $tan (sin^-1 x)$ ?

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Answer 1 · 2015-10-23T20:15:41

$tan ({sin}^{- 1} (x)) = \frac{x}{\sqrt{1 - x^{2}}}$ $tan(sin^(-1)(x)) = x/(sqrt(1-x^2)$

Explanation:

If ${sin}^{- 1} (x) = θ$ $sin^(-1)(x)=theta$
then
$XXX$ $color(white)("XXX")$ based on a unit circle (hypotenuse $= 1$ $= 1$ )
$XXX$ $color(white)("XXX")$ the side opposite $θ$ $theta$ will have a length of $x$ $x$
$XXX$ $color(white)("XXX")$ and
$XXX$ $color(white)("XXX")$ the adjacent side will have a length of $\sqrt{1 - x^{2}}$ $sqrt(1-x^2)$ (based on Pythagorean Theorem)

$tan ({sin}^{- 1} (x)) = tan (θ) = \frac{opposite}{adjacent} = \frac{x}{\sqrt{1 - x^{2}}}$ $tan(sin^(-1)(x)) = tan(theta) = ("opposite")/("adjacent") = x/(sqrt(1-x^2))$

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What is the value of $tan ({sin}^{- 1} x)$ $tan (sin^-1 x)$ ?

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