How do you verify $(1+sin theta)(1- sin theta) = cos^2 theta$ ?

Question

19561 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-15T00:23:57

$1 + sin theta - sin theta - sin^2theta = cos^2theta$

$1 - sin^2theta = cos^2theta$

Modifying the pythagorean identity $sin^2x + cos^2x = 1 -> cos^2x = 1 - sin^2x$ :

$cos^2theta = cos^2theta$

Identity proved!

Hopefully this helps!

How do you verify (1+sin theta)(1- sin theta) = cos^2 theta(1+sin theta)(1- sin theta) = cos^2 theta?