The value of (1 + cot θ – cosec θ) (1 + tan θ + sec θ) is
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Given: (1 + cotθ – cosecθ)(1 + tanθ + secθ).
1. Rewrite in terms of sinθ and cosθ:
(1 + cosθ/sinθ – 1/sinθ)(1 + sinθ/cosθ + 1/cosθ).
2. Simplify each factor:
First factor: (sinθ + cosθ – 1)/sinθ.
Second factor: (cosθ + sinθ + 1)/cosθ.
3. Multiply and simplify:
Numerator: (sinθ + cosθ)² – 1 = 2sinθcosθ.
Denominator: sinθcosθ.
4. Result: 2sinθcosθ / sinθcosθ = 2.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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