Sine Cosine Pythagorean Identity

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eliotmason
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Sine Cosine Pythagorean Identity

I am currently learning about Verifying trigonometric identities and it has been a really long time since I have taken any algebra. I wanted to know if I could modify the pythagorean identity to such:

So, the sine, cosine pythagorean identity is:

$\sin ^{2}\theta + \cos ^{2}\theta = 1$

so that means that this is also true:

$\cos ^{2}\theta = 1 - \sin^{2}\theta$

or...

$\cos ^{2}\theta = -\sin^{2}\theta + 1$

So here is my question. I don't remember if I am allowed to do this but does that mean that this can also be true? -->

$-\cos ^{2}\theta = \sin^{2}\theta - 1$

Posts: 136
Joined: Sun Feb 22, 2009 11:12 pm

Re: Sine Cosine Pythagorean Identity

$\sin ^{2}\theta + \cos ^{2}\theta = 1$

so that means that this is also true:

$\cos ^{2}\theta = 1 - \sin^{2}\theta$

$\cos ^{2}\theta = -\sin^{2}\theta + 1$

does that mean that this can also be true? --> $-\cos ^{2}\theta = \sin^{2}\theta - 1$
Yes:
-1(cos^2(@)) = -1(-sin^2(@) + 1
-cos^2(@) = +sin^2(@) - 1