How do you verify $cot^2 x/ (1+csc x) = (1-sin x)/ sin x$ ?

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Answer 1 · 2015-08-12T13:07:03

$sin^2 A + cos^2 A = 1$
Divide by $sin^2 A$
$1 + cot^2 A = csc^2 A$

$cot^2 x/(1+csc x) = (csc^2 x-1)/(1+csc x) = ((csc x-1)(csc x+1))/(1+csc x) = 1/sin x - 1 = (1 - sin x)/sin x$

How do you verify cot^2 x/ (1+csc x) = (1-sin x)/ sin xcot^2 x/ (1+csc x) = (1-sin x)/ sin x?