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I need help verifying a trig identity. I have tried several times. This question is totally different than what was presented in class (which the teacher didn't explain very well either).

Sec X + csc X

-------------------- = csc X

1 + tan X

To prove this identity, you need to rewrite sec X & csc X

as 1/cos X & 1/sin X respectively:

Sec X + csc X (1/cos X)+(1/sin X) (sin X+cos X)/(cos X sin X)

--------------- = -------------------------- = -----------------------------------

1 + tan X 1 + (sin X /cos X) (sin X+cos X)/ cos X

1/ (cos X sin X)

= -------------------- (Note that the sin X +cos X factor is eliminated)

1/ cos X

= 1/ sin X = csc X =RHS (shown)

Hope this helps. Peace.

Calculus

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