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Math Help - Confused about Pythagorean Identity

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    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?
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  2. #2
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    Re: Confused about Pythagorean identity

    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.
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    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.
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    Re: Confused about Pythagorean Identity

    Quote Originally Posted by daigo View Post
    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
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  5. #5
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    Re: Confused about Pythagorean Identity

    Specifically, x^2+ y^2 is NOT x^2- y^2!
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