Confused about Pythagorean Identity

**daigo** · May 14th 2012, 10:18 AM

I learned that sin^2(theta) + cos^2(theta) = 1, but for a problem we did, sin^2(15) - cos^2(15) = 1. I don't understand how this works, how do you use the Pythagorean Identity to manipulate the steps into getting 1?

**Sylvia104** · May 14th 2012, 10:27 AM

Use the identity $\cos^2\theta-\sin^2\theta=\cos2\theta.$ In your example, $\sin^215^\circ-\cos^215^\circ = -\cos30^\circ = -\frac{\sqrt3}2.$

**daigo** · May 14th 2012, 10:29 AM

Wait, so then we solved the problem incorrectly? the answer is not equal to 1? Ugh...I wish I knew when a solution was wrong...I spent all afternoon trying to decipher how the arrived was arrived at.

**skeeter** · May 14th 2012, 10:33 AM

Originally Posted by daigo

Wait, so then we solved the problem incorrectly? the answer is not equal to 1? Ugh...I wish I knew when a solution was wrong...I spent all afternoon trying to decipher how the arrived was arrived at.

yes ... you evaluated $\sin^2(15^\circ) - \cos^2(15^\circ)$ incorrectly