Question

prove sin^2 A + cos ^2A = 1

Answer 1

Step-by-step explanation:

$\sin( \alpha ) = \frac{opp \: side}{hypotenuse}$

$\cos( \alpha ) = \frac{adjacent \: side}{hypotenuse}$

${ \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} =$

${( \frac{opp \: side}{hypontenuse} )}^{2} + {( \frac{adj \: side)}{hypotenuse} )}^{2}$

$= \frac{ {oppside}^{2} + {adj \: side}^{2} }{ {hypotenuse}^{2} }$

Using Pythagoras Theorem we have

$= \frac{ {hypotenuse}^{2} }{ {hypotenuse}^{2} } = 1$

Hence proved