How do you simplify $cos ({tan}^{- 1} (\frac{2}{3}))$ $cos(tan^-1 (2/3))$ ?

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Answer 1 · 2016-05-13T05:41:45

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

Let $a = {tan}^{- 1} (\frac{2}{3})$ $a = tan^(-1)(2/3)$ . Tangent is positive in both the first and the

third quadrants.

The given expression is $cos a = \pm \frac{3}{\sqrt{13}}$ $cos a = +-3/sqrt 13$ .

Positive sign for a in the first quadrant and $-$ $-$ sign for a in the third quadrant..

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