Question

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`

Answer 1

`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`