1-cos square theta=sin square theta

Answer 1

left side = 1 - cosxcosx

right side = sinxsinx

show they're equal

draw a unit circle. its equation with cener at the origin is

x^2 + y^2 = 1^2 = 1 = radius squared

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

x = rcosx y = rsinx

rcos^2(x) + rsin^2(x) = r^2

divide by r

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

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

Answer 2

sin²(θ) + cos²(θ) = 1 [this is the trig identity known as the Pythagorean Identity]

1 - cos²(θ) = sin²(θ) [you obtain this by subtracting cos²(θ) from both sides]

Let me know if there's something else you need help with.