Proving Cosine Identity: Is cos(t+2π) the Same as cos(t)?

[Saladsamurai]

$$\cos (t)=\cos(t+2\pi)$$

I know it is kind of silly, but I need to do it.

I could have sworn that a sum formula would have worked, ie.,
$$\cos(\alpha+\beta)=\cos \alpha \cos \beta -\sin \alpha \sin \beta$$

but when I sub in $$t$$ and$$2\pi$$ for the RHS, I am getting $$-\cos t$$

Where did I go wrong...

Casey

Edit: IDK why LaTex alpha isn't showing on RHS

 

[dynamicsolo]

$$\cos (t)=\cos(t+2\pi)$$

I know it is kind of silly, but I need to do it.

I could have sworn that a sum formula would have worked, ie.,
$$\cos(\alpha+\beta)=\cos\alpha\cos\beta-\sin\alpha\sin\beta$$

but when I sub in $$t$$ and$$2\pi$$ for the RHS, I am getting $$-\cos t$$

Where did I go wrong...

Casey

What is cos (2 pi)? (You're going to kick yerself...)

P.S. One of the alphas wasn't displaying because you wrote "alpa"; the cos t didn't display because you left out a space between "cos" and "t"; TeX is unforgiving that way...

 

[Saladsamurai]

What is cos (2 pi)? (You're going to kick yerself...)

P.S. One of the alphas wasn't displaying because you wrote "alpa"; the cos t didn't display because you left out a space between "cos" and "t"; TeX is unforgiving that way...

Ouch! I did not know it was possible to kick myself there ...
+1

Thanks,
Casey