## Proof of Basic Trigonometric Identity

To prove the identity
$sin^2 x cos^2 x =1$
, draw a right angled triangle, let an angle be
$x$
and label the sides for that angle.

from Pythagoras Theorem
$opposite^2+adjacent^2=hypotenuse^2$

Now divide by
$hypotenuse^2$

$\frac{opposite^2}{hypotenuse^2}+\frac{adjacent^2}{hypotenuse^2}=1$

But
$\frac{opposite}{hypotenuse}=sin \: x, \frac{adjacent}{hypotenuse}=cos \: x$

Hence
$sin^2 x +cos^2 x =1$
.