# Pythagorean Identity question

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1. Oct 5, 2017

### AMan24

1. The problem statement, all variables and given/known data
sin2x + cos2x = 1

but would sin23x + cos23x = 1?

2. Relevant equations
none.

3. The attempt at a solution

I'm pretty sure sin23x + cos23x cant equal 1 otherwise the identity would probably be written as sin2cx + cos2cx = 1 and i've never seen it written like this.

I was doing a homework problem and i ended up in a situation where, if i could use sin2cx + cos2cx = 1, i'd get my answer. But im doing it differently than the book, so my way might be wrong

2. Oct 5, 2017

### phyzguy

When you write $\sin^2(x) + \cos^2(x) = 1$ are there restrictions on the values x can take? For example, could x = 3 * y?

3. Oct 5, 2017

### AMan24

no there are no restrictions, so that must mean it does work, or actually, you said x = 3y. Im not sure... theres no restrictions im aware of

4. Oct 5, 2017

### phyzguy

Right. It's true for any value of x.

5. Oct 5, 2017

### Ray Vickson

Take $x=10$. Would you agree that $\sin^2 10 + \cos^2 10 = 1?$ Do you really think that makes $\sin^2 30 + \cos^2 30$ come out different from 1? What about $\sin^2 37 + \cos^2 37?$ That would be $\sin^2 cx + \cos^2 cx$ with $c = 3.7$.

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