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.

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

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

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

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

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

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

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