sin^{2}x+cos^{2}x=1
Have you attempted a web search on the topic?
Prove the Pythagorean identity
$\sin\,x=\dfrac{opposite}{hypotenuse}$
$\sin^2\,x= \left( \dfrac{opposite}{hypotenuse} \right)^2$
$\cos\,x=\dfrac{adjacent}{hypotenuse}$
$\cos^2\,x= \left (\dfrac{adjacent}{hypotenuse} \right)^2$
$\sin\,x+\cos^2\,x= \left (\dfrac{opposite}{hypotenuse} \right)^2+ \left (\dfrac{adjacent}{hypotenuse} \right)^2$
$= \left (\dfrac{(opposite)^2+(adjacent )^2}{(hypotenuse)^2} \right)$
$=\dfrac{(hypotenuse)^2}{(hypotenuse)^2}$
$=1$