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

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Answer 1 · 2015-10-19T17:52:37

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:

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

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

$1 = ({sin}^{2}) x ({cos}^{2}) x$ $1=(sin^2)x(cos^2)x$
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How do you prove the identity (sin2)x(cos2)x=1(sin^2)x (cos^2)x=1 ?