Prove the following.
cot2θ – tan2θ = cosec2θ – sec2θ
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Solution
\[\cot^2 \theta - \tan^2 \theta\]
\[ = \left( {cosec}^2 \theta - 1 \right) - \left( \sec^2 \theta - 1 \right) \left( 1 + \tan^2 \theta = \sec^2 \theta \& 1 + \cot^2 \theta = {cosec}^2 \theta \right)\]
\[ = {cosec}^2 \theta - 1 - \sec^2 \theta + 1\]
\[ = {cosec}^2 \theta - \sec^2 \theta\]
Concept: Application of Trigonometry
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