Question

(1 + cot² θ) is equal to ______.

Options

• sin² θ

• cos² θ

• cosec² θ

• sec² θ

Answer 1

(1 + cot² θ) is equal to cosec² θ.

Explanation:

sin2 θ + cos2 θ = 1

`sin^2 θ/sin^2 θ + cos^2 θ/sin^2 θ`

= `1/sin^2 θ`

`sin^2 θ/sin^2 θ = 1`

`cos^2 θ/sin^2 θ = cot^2 θ`

since `cot θ = cos θ/sin θ`

`1/sin^2 θ = "cosec"^2 θ`

since cosec θ = `1/sin θ`

1 + cot² θ = cosec² θ