# ProveSin^a2+Cos^2a=1

lokesh
23 Points
9 years ago
sin(x)^2+cos(x)^2 = 1

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

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

cos(x - x) = 1 ....

Note: I'm using the Sum-Difference Identity: cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

cos( 0 ) = 1

1 = 1
37 Points
9 years ago
Thanks

Yash Baheti IIT Roorkee
9 years ago
Hi,

Take a right angled triangle.
Find the values of Sin and Cos in terms of , P, B, and H. Where P is perpendicular length, Bia base length and H is hypoteneous Length. Put the values in pythagoras theorem, you will get the identity.
Yugabrat Gogoi
47 Points
9 years ago
we know that sin= (opposite line of  a)/hypotenuse
so let sin be o/h

we know that cos=adjecent line to a/hypotenuse
so, let cos = a/h
sin2a+cos2a=1
lhs,
=(o/h)2+(a/h)2
=(o2+a2)/h2
=h2/h2                    [lets take ‘o’ as ‘a’ , ‘a’ as ‘b’ and hypotenuse as ‘c’ by using   =1                                                                  pytogorus theorum a2+b2=c2]

rhs
=1

therefore prooved sin2a+cos2a=1.

hope u like it .

regards Yugabrat Gogoi