How do I simplify trig identities involving (tan+1)^2 and secx+1/secx?

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SUMMARY

The discussion focuses on simplifying trigonometric identities involving the expressions (tan + 1)2 and (sec x + 1)/sec x over 1 + 1/sec2x. The user initially expands (tan + 1)2 to (tan + 1)(tan + 1) and attempts to apply the quotient identity, but encounters difficulties. The second expression's complexity arises from the presence of 1's, leading to confusion. Ultimately, the user successfully simplifies both identities with assistance from a forum member named cookiemaster.

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Dantes
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Hey everyone.

I am doing some trig homework questions over identities and like most people its driving me insane.

I have this one that has (tan+1)^2 and secx+1/secx over 1 + 1/sec^2x.

Now my issue on the first one is that I get it to (tan+1)(tan+1) and then take it into sin/cos+1 * sin/cos+1 using the quotient identity. and I get stuck.

On the 2nd one those 1's by themselves drive me crazy and I am not sure what to do with them.

Any help is appreciate been looking over these two problems for awhile and its giving me a headache.
 
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Both of the identities are equal to zero and I just am trying to simplify it down in terms of sin cos or tan.
 
nevermind got them done thanks to cookiemaster!
 

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