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Prove the following: (sinθ + cosecθ)2 + (cosθ + secθ)2 = tan2θ + cot2θ + 7 - Mathematics and Statistics

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Question

Prove the following:

(sinθ + cosecθ)² + (cosθ + secθ)²= tan²θ + cot²θ + 7

Sum

Solution

L.H.S. = (sinθ + cosecθ)² + (cosθ + secθ)²

= sin²θ + cosec²θ + 2sinθ cosecθ + cos²θ + sec²θ + 2cosθ secθ

= (sin²θ + cos²θ) + cosec²θ + 2 + sec²θ + 2

= 1 + (1 + cot²θ) + 2 + (1 + tan²θ) + 2

= tan²θ + cot²θ + 7

= R.H.S.

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Fundamental Identities

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Q 10) xi)Q 10) x)Q 10) xii)

Chapter 2: Trigonometry - 1 - MISCELLANEOUS EXERCISE - 2 [Page 34]

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Balbharati Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board

Chapter 2 Trigonometry - 1
MISCELLANEOUS EXERCISE - 2 | Q 10) xi) | Page 34

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