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Question
sec θ when expressed in term of cot θ, is equal to ______.
Options
`(1 + cot^2 θ)/cotθ`
`sqrt(1 + cot^2 θ)`
`sqrt(1 + cot^2 θ)/cotθ`
`sqrt(1 - cot^2 θ)/cotθ`
Solution
sec θ when expressed in term of cot θ, is equal to `underlinebb(sqrt(1 + cot^2 θ)/cotθ)`.
Explanation:
As we know that,
sec2 θ = 1 + tan2 θ
and cot θ = `1/tanθ`
`\implies` tan θ = `1/cotθ`
∴ sec2 θ = `1 + (1/cotθ)^2`
= `1 + 1/(cot^2 θ)`
`\implies` sec2 θ = `(cot^2 θ + 1)/(cot^2 θ)`
`\implies` sec θ = `sqrt(1 + cot^2 θ)/cotθ`
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