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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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