Prove the following identities I — task. Maths CBSE Live product, Class 10 (2026-27).

Using the trigonometric identities, show that \(\frac{1 - \tan^2 θ}{\cot^2 θ - 1} = \tan^2 θ\) .

Proof:

\begin{array}{l} LHS = \frac{1 - \tan^{2} θ}{\cot^{2} θ - 1} \\ = \frac{1 - \frac{i^{2} θ}{i^{2} θ}}{\frac{i^{2} θ}{i^{2} θ} - 1} \\ = \frac{\frac{i^{2} θ - \sin^{2} θ}{i^{2} θ}}{\frac{\cos^{2} θ - i^{2} θ}{i^{2} θ}} \\ = \frac{\sin^{2} θ}{i^{2} θ} \\ = i^{2} θ \end{array}

\(=RHS\)

Hence proved.

Did you find an error?

4. Prove the following identities I