How do you verify the identity $(csc x - cot x)^2 = (1 - cos x)/(1+cosx)$ ?

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Answer 1 · 2018-03-06T00:49:53

See below

$(csc-cotx)^2=(1-cosx)/(1+cosx)$
$(csc^2x-2cotxcscx+cot^2x)=(1-cosx)/(1+cosx)$
$(1/sin^2x-(2cosx)/sin^2x+cos^2x/sin^2x)=(1-cosx)/(1+cosx)$

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

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

$((cancel(1-cosx)(1-cosx))/(cancel(1-cosx)(1+cosx)))=(1-cosx)/(1+cosx)$

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

How do you verify the identity (csc x - cot x)^2 = (1 - cos x)/(1+cosx)(csc x - cot x)^2 = (1 - cos x)/(1+cosx)?