Surely you know that is NOT ...
Hello Everyone! Today we are asked to prove that both this expressions are true: and . To be quite honest, I am not very sure as to how I can prove these, but my attempt for the first one, I was able to prove that but was unsure as to how I would be able to turn it into which is what I need to prove the first equality.
As for the second one I did something like this:
So that:
and by properties of odd and even function:
Thus, it should be true to say that :
The proof above, for me, is quite sloppy, but I think I could live with that. But for the first one, I really have no idea as to how to prove it. Anyone got some ideas as to how I should prove both equivalence? Thanks everyone in advance!
Yeah, that's absolutely true,that's why I was unable to prove the equality. Here's how my little failed proof goes:
From the equation above, we can see that the modulus is 1 so that:
For the equation above to be true, the radicand should equal to 1, so that
From here, I tried to play with a lot of trig identities which all I was able to do is prove that this equation is true. But yeah, like Plato and Prove it said, this is not equal to
. So, anyone here have any idea as to how I should proceed with the proof? Thanks again to both of you!