$\"\"$

\

If $\"\"$ prove that $\"\"$ .

\

Definition of inverse trigonometric function : $\"\"$ .

\

$\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$ .

\

Chain rule of derivative: $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

From Pythagorean theorem,

\

The square of the hypotenuse is equal to sum the squares of the other two sides.

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ and $\"\"$ .

\

$\"\"$

\

$\"\"$ where $\"\"$

\

$\"\"$

\

$\"\"$ where $\"\"$ .