You are here:



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.


All Answers

Answers by Expert:

Ask Experts


Frederick Koh


I can answer questions concerning calculus, complex numbers, vectors, statistics , algebra and trigonometry for the O level, A level and 1st/2nd year college math/engineering student.


More than 7 years of experience helping out in various homework forums. Latest Presence is over at . You can also visit my main maths website where I have designed "question locker" vaults to store tons of fully worked math problems. A second one is currently being built. Peace.

IEEE(Institute of Electrical and Electronics Engineers )

Former straight As A level student from HCJC (aka HCI); scored distinctions in both C and Further Mathematics B Eng (Hons) From The National University Of Singapore (NUS) B Sc (Hons) From University of London External (Grad Route)

©2016 All rights reserved.