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Prove the Following.Secθ (1 – Sinθ) (Secθ + Tanθ) = 1 - Geometry

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Prove the following.
secθ (1 – sinθ) (secθ + tanθ) = 1

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Solution

\[\sec\theta\left( 1 - \sin\theta \right)\left( \sec\theta + \tan\theta \right)\]
\[ = \left( \sec\theta - \sec\theta\sin\theta \right)\left( \sec\theta + \tan\theta \right)\]
\[ = \left( \sec\theta - \frac{\sin\theta}{\cos\theta} \right)\left( \sec\theta + \tan\theta \right)\]
\[ = \left( \sec\theta - \tan\theta \right)\left( \sec\theta + \tan\theta \right)\]
\[ = \sec^2 \theta - \tan^2 \theta\]
\[ = 1 \left( 1 + \tan^2 \theta = \sec^2 \theta \right)\]

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 5.01 | Page 138
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