Question

prove that cos square a +sin square a=1

Answer 1

theta is written as @

cos^2@= [base/hypotenuse}^2

sin^2@=[height/hypotenuse}^2

on adding (by taking LCM) both they will like,

[base^2 + hiehgt^2}/(hypotenuse^2) -----------1 equation

as base^2 + hiehgt^2 = hypotenuse^2 ---------2equation

put the value of (base^2 + hiehgt^2) form 2equation in 1 equation

hypotenuse^2/hypotenuse^2 = 1

hence proved

Answer 2

de'moivers theorem states that
${e}^{i \alpha } = \cos( \alpha ) + i \sin( \alpha )$
now
${e}^{ - i \alpha } = \cos( \alpha ) - i \sin( \alpha )$
multiplying the two we get
$1 = { \cos( \alpha ) }^{2} - {i}^{2} { \sin( \alpha ) }^{ {}^{2} }$
this is equal to
${ \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} = 1$
hence proved