Maharashtra State BoardHSC Science (General) 11th
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Prove the following: (sinθ + cosecθ)2 + (cosθ + secθ)2 = tan2θ + cot2θ + 7 - Mathematics and Statistics

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Sum

Prove the following:

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

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Solution

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

= 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.

Concept: Fundamental Identities
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 2 Trigonometry - 1
Miscellaneous Exercise 2 | Q 10. (xi) | Page 34
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