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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.


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Frederick Koh


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