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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`
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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`
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