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Prove the Following. Cot2θ – Tan2θ = Cosec2θ – Sec2θ - Geometry

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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APPEARS IN

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board
Chapter 6 Trigonometry
Problem Set 6 | Q 5.04 | Page 138
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