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  
\[sin^2 x +cos^2 x =1\]
.

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