Prove-that-tan-sec-1-tan-tan-1-cot-

Question Number 10542 by FilupS last updated on 17/Feb/17

Prove that :

\tan (\sec^{- 1} (\sqrt{\tan (θ)})) = \sqrt{\tan (θ)} \sqrt{1 - \cot (θ)}

Answered by mrW1 last updated on 17/Feb/17

l e t α = \sec^{- 1} (\sqrt{\tan (θ)})

\Rightarrow \sec α = \sqrt{\tan (θ)}

\Rightarrow \sec^{2} α = \tan (θ)

\tan (\sec^{- 1} (\sqrt{\tan (θ)})) = \tan α = \sqrt{\sec^{2} α - 1} = \sqrt{t a n (θ) - 1} = \sqrt{\tan (θ) [1 - \frac{1}{\tan (θ)}]} = \sqrt{\tan (θ)} \sqrt{1 - \cot (θ)}

p r o v e n!

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