How do you verify $(tanθ – sinθ • cosθ) / (sin²θ) = tanθ$ ?

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Answer 1 · 2016-05-02T21:35:53

see below

Left Side $=(tan theta-sin theta cos theta)/sin^2 theta$

$=(tan theta-cos theta tan theta * cos theta)/sin^2 theta$ --> $sin theta = cos theta tan theta$

$=(tan theta-tan theta cos^2 theta)/sin^2 theta$

$=(tan theta(1-cos^2 theta))/sin^2 theta$

$=(tan theta sin^2 theta)/sin^2 theta$

$=tan theta$

$=$ Right Side

How do you verify (tanθ – sinθ • cosθ) / (sin²θ) = tanθ(tanθ – sinθ • cosθ) / (sin²θ) = tanθ?