Answer
See below.
Work Step by Step
$LHS=\frac{tan\theta-cot\theta}{tan\theta+cot\theta}
=\frac{tan\theta-cot\theta}{tan\theta+cot\theta}\times\frac{sin\theta cos\theta}{sin\theta cos\theta}
=\frac{sin^2\theta-cos^2\theta}{sin^2\theta+cos^2\theta}
=sin^2\theta-cos^2\theta
=1-2cos^2\theta
=RHS$
