How do you prove that #(csc x - cot x)^2 = (1 - cos x)/(1+cosx) #?

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Answer 1 · 2015-12-12T04:53:38

Only modify the left side.

#(cscx-cotx)^2=csc^2x-2cscxcotx+cot^2x#

#=1/sin^2x-2(1/sinx)(cosx/sinx)+cos^2x/sin^2x#

#=(1-2cosx+cos^2x)/(sin^2x)#

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

#=(1-cosx)^2/((1+cosx)(1-cosx)#

#=(1-cosx)/(1+cosx)#