How do you prove this identity #3/(1-cos(a)) +3/(1+sin(a)) =6csc^2(a)#?

1 Answer
Mar 25, 2018

See below

Explanation:

Using the identities:
#1-cos^2a= sin^2a#
#1/sina= csca#

It can't be proved...but assuming you made a typo and it says:

#3/(1-cosa)+3/(1+cosa)= 6csc^2a#

Get a common denominator:
#(3(1+cosa))/((1-cosa)(1+cosa))+(3(1-cosa))/((1+cosa)(1-cosa))= 6csc^2a#

#(3+3cosa)/(1-cos^2a)+(3-3cosa)/(1-cos^2a)= 6csc^2a#

#6/(1-cos^2a)=6csc^2a#

#6/(sin^2a)=6csc^2a#

#6csc^2a=6csc^2a#