How do you evaluate $tan ({sin}^{- 1} (\frac{2}{3}))$ $Tan (sin^-1 (2/3))$ ?

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How do you evaluate $tan ({sin}^{- 1} (\frac{2}{3}))$ $Tan (sin^-1 (2/3))$ ?

1 Answer

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Answer 1 · 2016-11-12T06:52:51

Conventional value is $\frac{2}{\sqrt{5}}$ $2/sqrt5$ and the general value is $\pm \frac{2}{\sqrt{5}}$ $+-2/sqrt5$ .

Explanation:

Let $a = {sin}^{- 1} (\frac{2}{3}) \in Q_{1}$ $a=sin^(-1)(2/3) in Q_1$ for the conventional principal value and

also $\in Q_{2}$ $in Q_2$ , for the general value.

The given expression is tan a

$= \frac{sin a}{cos a} = \frac{\frac{2}{3}}{\pm \sqrt{1 - {(\frac{2}{3})}^{2}}} = \pm \frac{2}{\sqrt{5}}$ $=sin a/cos a=(2/3)/(+-sqrt(1-(2/3)^2))=+-2/sqrt5$ .

Conventional value is $\frac{2}{\sqrt{5}}$ $2/sqrt5$ and the general value is $\pm \frac{2}{\sqrt{5}}$ $+-2/sqrt5$ .

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