Question

`sqrt(sec^2 θ + cocec^2 θ)` is equal to ______.

Options

• sin cos θ

• 1

• 0

• secθ cosec θ

Answer 1

`sqrt(sec^2 θ + cocec^2 θ)` is equal to sec θ cosec θ.

Explanation:

sec θ = `1/cos θ` and cosec θ = `1/sin θ`

`sqrt(sec^2 θ + cocec^2 θ) = sqrt(1/cos^2 θ + 1/sin^2 θ)`

= `sqrt((sec^2 θ + cos^2 θ)/(cos^2 θ .sin^2 θ))`

= `sqrt(1/(cos^2 θ .sin^2 θ))`

= `1/(cos θ.sin θ)`

= `(1/cos θ)(1/sin θ)`

= secθ cosec θ