Proving Trig Identity Question

[SharkFin39]

Well, I've been working on some Trigonometric Identity Proofs now for about five to six hours. However, I have come across one which has me absolutely stumped. I've tried just about everything I can think of and have had no success. Perhaps someone can point me in the right direction? Here is the problem I'm working with.

1 + sin^2x = sec^2x + sin^2x - sin^2x X sec^2x

Since I am having trouble typing it out, that is a multiplication sign between the last two terms.

I've been working with the right side of the equation for the most part. I've tried changing everything to sins and cosines, I've tried pythagorian idents., but am not having any luck. Perhaps it is an algebraic problem I'm having. If anyone can help with this I'd greatly appreciate it. Thanks in advance!

Shark

 

[Unco]

1 + sin^2(x) = sec^2(x) + sin^2x - sin^2(x) * sec^2(x)

Simplify sin^2(x) * sec^2(x).

Then there's an identity in the RHS which becomes visible.

 

[SharkFin39]

Unbelievable.... I can't see how I missed that for so long. Guess I was just looking at it for too long and developed some sort of mental block. Oh well, now its complete and I can sleep easy tonight. Thank you very much for your help, it is greatly appreciated.

Thanks again,
Shark