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Question
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")`
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")`
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