Consider writing:
Now rewrite the two terms, and then apply a Pythagorean identity.
It's me again and I've got another problem that I've been working on for two days, and I just can't get started on it!
Prove the identity (1 - tan^2x ) / (1 + tan^2x) = 1 - 2sin^2x.
So what I have so far is:
(1 - tan^2x) / (sec^2x)
Now what I do next?
Ok, so now the Pythagorean identity is cos^2x + sin^2x = 1.
What we have so far is cos^2 - sin^2, yes? Now... I feel so dumb and stupid, I must have some mental deficiency but I just can't seem to relate the two. Please show me how, and I'll study it till I get it.
Ah, it's just a question of logic, isnt it? I don't know why I have none. Well, just gotta work at it! Thank you very much, I understand it now, but I'll go through this example over and over.
So, all I need to know is these 2 rules:
tanx = sinx / cosx
cos^2x + sin^2x = 1
And then, just apply it everywhere. Ok.
Another update for all my avid readers: just did two more examples, and got them quick and easy! I don't know what happened, but it seems I suddenly acquired the wonderful skill of logic.
I won't post again, I just wanted to express my thanks for the helpfulness of this board.