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Prove the Following.Sec2θ + Cosec2θ = Sec2θ × Cosec2θ - Geometry

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Sum

Prove the following.
sec2θ + cosec2θ = sec2θ × cosec2θ 

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Solution

\[\sec^2 \theta + {cosec}^2 \theta\]
\[ = \frac{1}{\cos^2 \theta} + \frac{1}{\sin^2 \theta}\]
\[ = \frac{\sin^2 \theta + \cos^2 \theta}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta \sin^2 \theta}\]
\[ = \frac{1}{\cos^2 \theta} \times \frac{1}{\sin^2 \theta}\]
\[ = \sec^2 \theta  \text{ cosec }^2 \theta\]
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 5.03 | Page 138
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