How do you prove the identity (sin^2)x (cos^2)x=1 ?

Explanation:

Sin and cos form the two legs (b) and (c) of a right triangle, and it's hypotenuse (a) is the radius of the trigonometric circle (r = a = 1).

According to Pythagoras:

${a}^{2} = {b}^{2} + {c}^{2}$

${1}^{2} = \left({\sin}^{2}\right) x \left({\cos}^{2}\right) x$

$1 = \left({\sin}^{2}\right) x \left({\cos}^{2}\right) x$