Prove that # sqrt((1-cosx)/(1+cosx)) -= (1-cosx)/(|sinx|) # ?
2 Answers
Feb 14, 2018
Please see below.
Explanation:
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Feb 14, 2018
We seek to prove that:
# sqrt((1-cosx)/(1+cosx)) -= (1-cosx)/(|sinx|) #
Consider the RHS:
# RHS = (1-cosx)/(|sinx|) #
# \ \ \ \ \ \ \ \ = sqrt( ((1-cosx)/(|sinx|))^2 ) #
# \ \ \ \ \ \ \ \ = sqrt( (1-cosx)^2/(sin^2x) ) #
# \ \ \ \ \ \ \ \ = sqrt( (1-cosx)^2/(1-cos^2x) ) #
# \ \ \ \ \ \ \ \ = sqrt( (1-cosx)^2/((1+cosx)(1-cosx) ) #
# \ \ \ \ \ \ \ \ = sqrt( (1-cosx)/(1+cosx) ) #
# \ \ \ \ \ \ \ \ = LHS \ \ \ \ # QED