1-cos square theta=sin square theta

Answer 1

use law of cosines

c^2 = a^2 + b^2 - 2abcosC where C = pi/2 then

c^2 = a^2 +b^2 as cosC = 0

r^2 = x^2 + y^2 convert to polar form where r^2 = x^2+y^2

x = rcosT y = rsinT

let r = 1

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

subtract cos^2(T) from both sides

1- cos^2(T) = sin^2(T)

Answer 2

This is just the Pythagorean identity with an algebraic rearrangement.

sin²(θ) + cos²(θ) = 1.