prove-that-sec-tan-1-x-x-2-1-

Question Number 182842 by malwan last updated on 15/Dec/22

p r o v e t h a t

s e c ({t a n}^{- 1} x) = \sqrt{x^{2} + 1}

Answered by cortano1 last updated on 15/Dec/22

l e t x = \tan t

\sqrt{x^{2} + 1} = \sqrt{\tan^{2} t + 1} = \sqrt{\sec^{2} t} = \sec t

\Rightarrow \sec (\tan^{- 1} (\tan t)) = \sec t

Commented by malwan last updated on 15/Dec/22

t h a n k y o u s i r

Answered by BaliramKumar last updated on 15/Dec/22

L H S = s e c ({t a n}^{- 1} x)

L H S = \sqrt{{s e c}^{2} ({t a n}^{- 1} x)}

L H S = \sqrt{{t a n}^{2} ({t a n}^{- 1} x) + 1}

L H S = \sqrt{x^{2} + 1} = R H S

Commented by malwan last updated on 15/Dec/22

t h a n k y o u s o m u c h

Answered by manxsol last updated on 16/Dec/22

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