You can put this solution on YOUR website! You can start working on the left side to get the right side of the equation.
(tan x - sin x)/(sin^3 x)
=(sin x/cos x - sin x)/sin^3 x
=(sin x -sin x cos x)/cos x * sin^3 x
Factor the numerator by sin x and split the denominator's sin^3 into sin^2 * sin x:
=sin x(1-cos x)/(cos x * sin x * sin^2 x)
=(1 - cos x)/cos x(1-cos^2 x)
Factor the denominator:
=(1 - cos x)/cos x * (1 + cos x)(1 - cos x)
=1/cos x(1 +cos x)
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