Question

Prove the identity cos^2 theta + sin^2 theta = 1 .

Answer 1

consider a right angled triangle abc name h=hypotenuse,b=base,p=perpendicular
therefore,

sin(x)=p/h , cos(x)=b/h

BY PYTHAGORAS THEOREM WE KNOW THAT

H^2=P^2+B^2 -------(1)

THEREFORE,

p=h.sin(x) ------(2)
b=h.cos(x) -------(3)

put values of 2 and 3 in eq 1,then we get

h^2={h.sin(x)}^2 + {h.cos(x)}^2

h^2={h^2.sin^2(x)} + {h^2.cos^2(x)}

taking common from RHS
WE GET,

h^2=h^2 {sin^2(x) + cos^2(x)}
h^2/h^2=sin^2(x)+cos^2(x)

1=sin^2(x) + cos^2(x)

I HOPE IT HEPLS.