Maharashtra State BoardHSC Science (General) 11th
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Select the correct option from the given alternatives: If cosecθ + cotθ = 52, then the value of tanθ is - Mathematics and Statistics

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MCQ

Select the correct option from the given alternatives:

If cosecθ + cotθ = `5/2`, then the value of tanθ is

Options

  • `14/25`

  • `20/21`

  • `21/20`

  • `15/16`

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Solution

`20/21`

Explanation:

cosecθ + cotθ = `5/2`                        ....(i)

cosec2θ - cot2θ = 1

∴ (cosecθ + cotθ) (cosecθ − cotθ) = 1

∴ `5/2` (cosecθ − cotθ) = 1

∴ cosecθ − cotθ = `2/5`                     ...(ii)

Subtracting (ii) from (i), we get

2cotθ = `5/2-2/5=21/10`

∴ cotθ = `21/20`

∴ tanθ = `20/21`

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. (6) | Page 33
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