1. ## Confused about Pythagorean Identity

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?

2. ## Re: Confused about Pythagorean identity

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

3. ## Re: Confused about Pythagorean Identity

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.

4. ## Re: Confused about Pythagorean Identity

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 $\displaystyle \sin^2(15^\circ) - \cos^2(15^\circ)$ incorrectly

5. ## Re: Confused about Pythagorean Identity

Specifically, $\displaystyle x^2+ y^2$ is NOT $\displaystyle x^2- y^2$!