$\displaystyle sec^2{x}+tan^2{x}sec^2{x}=sec^4{x}$

So far I have changed everything to fractions using the quotient properties, but I have no idea where to go next.

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- Feb 15th 2011, 08:43 PMtoekneeHelp with Trigonometric Identities
$\displaystyle sec^2{x}+tan^2{x}sec^2{x}=sec^4{x}$

So far I have changed everything to fractions using the quotient properties, but I have no idea where to go next. - Feb 15th 2011, 08:46 PMProve It
Use the identity $\displaystyle \displaystyle \tan^2{x} + 1 = \sec^2{x} \implies \tan^2{x} = \sec^2{x} - 1$.

Substitute this into the LHS and simplify. - Feb 15th 2011, 08:57 PMtoeknee
Sorry, but what does LHS stand for?

- Feb 15th 2011, 09:02 PMtopsquark
- Feb 15th 2011, 09:02 PMProve It
Left Hand Side

- Feb 15th 2011, 09:10 PMtoeknee
You can still use the Pythagorean property for $\displaystyle tan^2{x}sec^2{x}$?

- Feb 15th 2011, 09:14 PMProve It
Surely $\displaystyle \displaystyle \tan^2{x}\sec^2{x} = (\sec^2{x} - 1)\sec^2{x}$...

- Feb 15th 2011, 09:18 PMtoeknee
I thought because it was one term, you couldn't, but I guess not. Thanks a lot for your help. Kind of fitting that your name is Prove It.