Question

Prove that 1-tan 2 o/cot 2 o-1=tan 2 0

Answer 1

(1-tan2θ)/(cot2θ-1)
=(1-sin2θ/cos2θ)/(cos2θ/sin2θ-1)
={(cos2θ-sin2θ)/cos2θ}/{(cos2θ-sin2θ)/sin2θ}
={(cos2θ-sin2θ)/cos2θ}×{sin2θ/(cos2θ-sin2θ)}
=sin2θ/cos2θ
=tan2θ (proved)

Answer 2

Given that
$\frac{1-tan2\theta}{Cot2\theta - 1}$
We know that, 

Cot2θ can be written as 1/Tan2θ

$\frac{1-tan2\theta}{ \frac{1}{Tan2\theta} - 1}$

$\frac{1-tan2\theta}{ \frac{1-Tan2\theta}{Tan2\theta} }$

$\frac{1-tan2\theta}{1-Tan2\theta}*Tan2\theta}$

$Tan2\theta}$