Question

If θ is acute and `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3, then θ is equal to ______.

Options

• 60°

• 30°

• 90°

• None of these

Answer 1

If θ is acute and `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3, then θ is equal to 60°.

Explanation:

We have `(cos^2θ)/(cot^2 θ - cos^2 θ)` = 3

`\implies` cos² θ = 3(cot² θ – cos² θ)

`\implies` cos² θ = 3 cot² θ – 3 cos² θ

`\implies` 4 cos² θ = 3 cot² θ

`\implies` 4 cos² θ = `(3 cos^2 θ)/(sin^2 θ)`

`\implies` sin² θ = `3/4`

`\implies` sin θ = `sqrt(3)/2`

`\implies` θ = 60°