trig...

Hi
I'm having some trouble simplifying this:

1-cos x + tan^2 x - sec^2 x
---------
sin^2 x

I know that tan^2 - sec^2 x = -1
but I don't know what to do after getting

1-cos x
--------- - 1
sin^2 x

Hello, lotmasta!

I don't know what to do after getting

1-cos x
--------- - 1
sin^2 x

Click to expand...

We can simplify it a bit more . . . but it's not very satisfying.

. . . 1 - cos x . . . . . . . . . . . .1 - cos x . . . . . . . . . . . . . . 1
. . . ------------ - 1 . = . -------------------------- - 1 . = . ------------ - 1
. . . 1 - cos²x . . . . . . . (1 - cos x)(1 + cos x) . . . . . . 1 + cos x


Get a common denominator and combine:

. . . . . . .1 . . . . 1 + cos x . . . . .1 - 1 - cos x . . . . . - cos x
. . . ------------ - ------------ . = . ---------------- . = . ------------
. . . 1 + cos x . .1 + cos x . . . . . .1 + cos x . . . . . 1 + cos x

. . . and that's all we can do.