How do you find the value of $cos ({tan}^{- 1} (\frac{2}{3}))$ $cos (tan^-1 (2/3))$ ?

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How do you find the value of $cos ({tan}^{- 1} (\frac{2}{3}))$ $cos (tan^-1 (2/3))$ ?

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Answer 1 · 2016-04-19T04:45:45

$\pm \frac{3}{\sqrt{13}}$ $+-3/sqrt13$

Explanation:

Let $a = {tan}^{- 1} (\frac{2}{3})$ $a =tan^(-1)(2/3)$ .
As tan a = 2/3, cos a and sin a should both have the same sign and $a = {tan}^{- 1} (\frac{2}{3}) = {33.7}^{o} or {213.7}^{o}$ $a = tan^(-1)(2/3)=33.7^o or 213.7^o$ , in $[0, 2 π]$ $[0, 2pi]$ .

So, I take a as either, and so, $cos a = cos ({tan}^{- 1} (\frac{2}{3})) = \pm \frac{3}{\sqrt{13}}$ $cos a = cos(tan^(-1)(2/3))=+-3/sqrt13$ .

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How do you find the value of $cos ({tan}^{- 1} (\frac{2}{3}))$ $cos (tan^-1 (2/3))$ ?

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