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`

Answer 1

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`