#### Question

Prove the following.

cot^{2}θ – tan^{2}θ = cosec^{2}θ – sec^{2}θ

#### Solution

\[\cot^2 \theta - \tan^2 \theta\]

\[ = \left( {cosec}^2 \theta - 1 \right) - \left( \sec^2 \theta - 1 \right) \left( 1 + \tan^2 \theta = \sec^2 \theta \& 1 + \cot^2 \theta = {cosec}^2 \theta \right)\]

\[ = {cosec}^2 \theta - 1 - \sec^2 \theta + 1\]

\[ = {cosec}^2 \theta - \sec^2 \theta\]

Is there an error in this question or solution?

Solution Prove the Following. Cot2θ – Tan2θ = Cosec2θ – Sec2θ Concept: Application of Trigonometry.