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

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Question

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

Solution

\[\left( \sec\theta + \tan\theta \right)\left( 1 - \sin\theta \right)\]

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

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

\[ = \frac{1 - \sin^2 \theta}{\cos\theta}\]

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

\[ = \cos\theta\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Problem set 6 | Q: 5.02 | Page no. 138
Solution Prove the Following.(Secθ + Tanθ) (1 – Sinθ) = Cosθ Concept: Application of Trigonometry.
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