Use double-angle or half-angle formula to simplify #(2-csc^2(x))/(csc^2(x))# ?

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Answer 1 · 2017-11-16T13:25:31

#(2-csc^2x)/csc^2x=-cos2x#

We have #csc^2x=1/sin^2x#

Then #(2-csc^2x)/csc^2x#

#=(2-1/sin^2x)/csc^2#

#=((2sin^2x-1)/sin^2x)/(1/sin^2x)#

#=2sin^2x-1#

#=-(1-2sin^2x)#

#=-cos2x#