please help with cos^4x(1+tan^2x)+sin^2x

[arcticknock]

Hi there
Help please with my homework!
cos^4x(1+tan^2x)+sin^2x
I'd really appreciate your help if you did! Thanks

 

[Quaid]

cos^4x(1+tan^2x)+sin^2x

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What have you tried (or thought about) so far?

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Thank you :cool:

 

[Mathesy]

Hi there
Help please with my homework!
cos^4x(1+tan^2x)+sin^2x
I'd really appreciate your help if you did! Thanks

I believe you need this simplified? If so, here it goes:

Remember, always use the "connectors". What can you use to help you simplify certain factors, so you can cancel them with the existing ones. What can you group? And so on, and so forth. Here, we see 1+tan^2x, which using the trig identities equals sec^2x. So, now you have cos^4x(sec^2x)+sin^2x.

Furthermore, you see the connection between the secant and cosine, which is secx=1/cosx, so sec^2x=1/cos^2x. Now, you can cancel out the cos^2x out of the cos^4x, and you get cos^2x+sin^2x as your result.

This is not the end, and you can simply say that cos^2x+sin^2x=1, since that is the pythagorean identity, and 1 is your final result.

Hope this helps. You have probably been helped on this one already, but it good for future references to have it worked out.

P.S. If there are still dilemmas, or questions regarding this problem, go ahead and ask!