1. ## Proving trig identities

I'd really appreciate someone telling me the right answer. My brain is way to tired to figure it out (or understand an explanation).

Thanks

2. Originally Posted by stache31

I'd really appreciate someone telling me the right answer. My brain is way to tired to figure it out (or understand an explanation).

Thanks
#1 and #3 are proven correctly.

To see why #2, and #4 are wrong:
For #2: $\frac{1}{2}[e^{-x} + e^{-(-x)}] \neq \frac{1}{2}(e^{-x} - e^x)$

For #4: $\frac{1 + \tanh{x}}{1 - \tanh{x}} = \frac{\cosh{x} + \sinh{x}}{\cosh{x} - \sinh{x}} \neq \frac{\cosh{x} - \sinh{x}}{\cosh{x} + \sinh{x}}$

You may want to refer to: Hyperbolic function as these proofs are very easy to verify.