Question

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is ______.

Options

• tan² θ

• sec² θ

• 1

• –1

Answer 1

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`, in simplified form, is –1.

Explanation:

`(cos^2 θ)/(sin^2 θ) - 1/(sin^2 θ)`

= `(cos^2 θ - 1)/(sin^2 θ)`

= `(-sin^2 θ)/(sin^2 θ)`       ...(∵ sin²θ = 1 – cos²θ)

= –1