Question

$1 - tan ^2 \div \cot ^2 - 1 = \tan ^{2}$

Answer 1

(1 - tan^2 theta) / (cot^2 theta - 1)
= 1 - (sin^2/cos^2) / (cos^2/sin^2 - 1)
= [(cos^2 - sin^2)/cos^2] / [(cos^2 - sin^2)/sin^2]
= tan^2 theta [Proved]

Hope it helps you .