How do you prove $sec^-1x+csc^-1x=pi/2$ ?

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Answer 1 · 2016-10-20T16:28:50

Please see the explanation.

Prove:

$sec^-1(x) + csc^-1(x) = pi/2$

Use the identity $csc^-1(x) = pi/2 - sec^-1(x)$ :

$sec^-1(x) + pi/2 - sec^-1(x) = pi/2$

$pi/2 = pi/2$

Q.E.D.

Answer 2 · 2016-10-20T17:15:46

use the fact that csc is the complementary function of sec.

let
$sec^-1x=y$

$=>x=secy$

$=>x=csc(pi/2-y)$
$=>csc^-1x=pi/2-y$

substituting back for y

$csc^-1x=pi/2-sec^-1x$

hence $sec^-1x+csc^-1x=pi/2$

as required.

How do you prove sec^-1x+csc^-1x=pi/2sec^-1x+csc^-1x=pi/2?