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?

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- May 14th 2012, 10:18 AMdaigoConfused 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?

- May 14th 2012, 10:27 AMSylvia104Re: Confused about Pythagorean identity
Use the identity $\displaystyle \cos^2\theta-\sin^2\theta=\cos2\theta.$ In your example, $\displaystyle \sin^215^\circ-\cos^215^\circ = -\cos30^\circ = -\frac{\sqrt3}2.$

- May 14th 2012, 10:29 AMdaigoRe: 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.

- May 14th 2012, 10:33 AMskeeterRe: Confused about Pythagorean Identity
- May 15th 2012, 10:19 AMHallsofIvyRe: Confused about Pythagorean Identity
Specifically, $\displaystyle x^2+ y^2$ is NOT $\displaystyle x^2- y^2$!