Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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Prove the Following.Secθ (1 – Sinθ) (Secθ + Tanθ) = 1 - Geometry

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Question

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

Solution

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

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Solution Prove the Following.Secθ (1 – Sinθ) (Secθ + Tanθ) = 1 Concept: Application of Trigonometry.
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