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NBSchile · May 24, 2012, 02:04 PM

Prove that sec^2 x - sin^2 x - cos^2 x = tan^2 x with your steps

Curlyben · May 24, 2012, 02:05 PM

What have you done so far ?

NBSchile · May 24, 2012, 02:10 PM

Originally Posted by Curlyben

What have you done so far ?

1 _ sin^2 x _ cos^2 x
------- ---------- ------------ = tan^2 x
cos^2 x 1 1

1 - sin^2 x cos^2 x - (cos^2 x)^2
-------------------------------------------------- =tan^2 x
cos^2 x

ebaines · May 24, 2012, 02:23 PM

Try this: note that -sin^2x - cos^2x = -(sin^2x + cos^2x). Do you recall what sin^2x + cos^2x equals? You can probably finish it from here.

NBSchile · May 24, 2012, 02:26 PM

Originally Posted by Curlyben

What have you done so far ?

In attachment

NBSchile · May 24, 2012, 02:31 PM

Thank You. Disregard that last comment. I saw that it formatted it weird so I put it in an attachment.

ebaines · May 24, 2012, 02:45 PM

Originally Posted by NBSchile

Thank You. Disregard that last comment. I saw that it formatted it weird so i put it in an attachment.

Looks like you multiplied through by cos^2x/cos^2x, but there's really no need to do that. Simply replace the -sin^2x-cos^2x terms with -1. Then combine that with 1/cos^2x:

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

You can finish it from here.