sin(x)/1-cos(x) + tan(x)/1+cos(x) = cos^2(x)+1/sin(x)cos(x)
sin x / (1 - cos x) + tan x / ( 1 + cos x) = multiply both parts of the first fraction by 1 + cos x and both parts of the second fraction by 1 - cos x; common denominator is 1 - cos^2 x = sin^2 x
[(sin x + sin x cos x) + tan x ( 1 - cos x)] / (1 - cos^2 x) = tan x cos x = sin x
(sin x + sin x cos x + tan x - sin x) / (sin^2 x) =
(sin x cos x + sin x / cos x) / sin^2 x = (cos x + 1 / cos x) / sin x = (cos^2 x + 1) / (sin x cosx)
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