Maharashtra State BoardHSC Science (Electronics) 11th
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Select the correct option from the given alternatives: If cosecθ − cotθ = q, then the value of cot θ is - Mathematics and Statistics

MCQ

Select the correct option from the given alternatives:

If cosecθ − cotθ = q, then the value of cot θ is

Options

  • `(2"q")/(1 + "q"^2)`

  • `(2"q")/(1 - "q"^2)`

  • `(1 - "q"^2)/(2"q")`

  • `(1 + "q"^2)/(2"q")`

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Solution

`(1 - "q"^2)/(2"q")`

Explanation:

cosecθ − cotθ = q ....(i)

cosec2θ − cot2θ = 1

∴ (cosecθ + cotθ) (cosecθ − cotθ) = 1

∴ (cosecθ + cotθ) q = 1

∴ cosecθ + cotθ = `1/"q"` ...(ii)

Subtracting (i) from (ii), we get

2cotθ = `1/"q"-"q"`

∴ cotθ = `(1-"q"^2)/(2"q")`

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 I. (8) | Page 33
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