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Answer 1 · 2017-11-05T15:17:21

#sec^2(x/2) = (csc^2x)(2-2cosx) #

#sec^2(x/2)# = #1/cos^2(x/2)#

Half angle identity forumla = # cos^2(a/2)=(1+cos(a))/2 #

#1/(1+cos(a))/2#= #2/(1+cos(x)#

Then multiply both numerator and denominator by 1-cos(x)

Resulting to

#(2-2cos(x))/(1-cos^2(x)#

Then with the identity

#sin^2=1-cos^2 #

The final result will be

#(2-2cos(x))/(sin^2(x))# = # (2-2cos(x))csc^2(x)#