Use trig. Identities to simplify: 1-(1/cos^2(x))?

Question

I'm sure I'm missing some silly little pattern in these problems, but I'm stuck on this one, lol. =) Any help and shortcuts/advice would be more than welcome. Thank you!

Answer 1

ok i will help you
first thing to do is....

cos^2(x)-1
---------------
cos^2(x)

and you should know that
cos^2(x)+sin^2(x)=1
cos^2(x)-1= -sin^2(x)

ok now put this on the first equation


- sin^2(x)
-------------
cos^2(x)

it is equal to -tan^2(x)

Hope this helps

Answer 2

1-(sec^2(x)) Using the reciprical identities, because 1/(cos(x)) = sec(x). Works for squared functions too.

1-sec^2(x) = -tan^2(x) Using the Pathagorean Identies, because 1+ tan^2(x) = sec^2(x). Use algebra.

Or you could just leave it at 1-sec^2(x). Either way is a good answer. Any more questions, and you could just e-mail me at [e-mail]. Good luck.

Answer 3

Yes, there is a silly pattern on this one.
The term in ( ) is sec^2 x in disguise, and then 1-sec^2 x is Tan^2 x in disguise. Sneaky these answer-producers.