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About Steve Holleran
Expertise
I can help with all math questions from basic math to Calculus. Whether it`s consumer questions, or questions from high school or college students, I have probably dealt with it at some time in my career.

Experience
33 years teaching experience in NJ public schools

Education/Credentials
B.S. Mathematics : Wake Forest University 1972 M.S. Mathematics : Monmouth University 1981

You are here: Experts > Science > Mathematics > Advanced Math > trig

Topic: Advanced Math

Expert: Steve Holleran
Date: 5/7/2008
Subject: trig

Question
Verify the identity: 1/1+cost=(csct-cott)csct

Answer
Hi Robert,

Okay, so we've got

                     1 / (1 + cos t) = (csc t - cot t) * csc t

I would work the right side, changing all the expressions back in terms of sines and cosines:

Right: (csc t - cot t)* csc t = (1/sin t - cos t / sin t) * 1/sin t

          = ( (1 - cos t)/ sin t) * 1/sin t

          = (1 - cos t) / sin^2 t

          = (1 - cos t) / (1 - cos^2 t)     Pythagorean identity

          = (1 - cos t) / [(1 - cos t)(1 + cos t)]

Now cancel the 1 - cos t factors and you have it.

Steve

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