Question

`sqrt((1 - cos^2theta) sec^2 theta) = tan theta` 

Options

• True

• False

Answer 1

This statement is True.

Explanation:

`sqrt((1 - cos^2 theta) sec^2 theta)`

= `sqrt(sin^2 theta * sec^2 theta)`   ...[∵ sin²θ + cos²θ = 1]

= `sqrt(sin^2 theta * 1/(cos^2 theta)`  ...`[∵ sec theta = 1/costheta, tan theta = sin theta/cos theta]`

= `sqrt(tan^2 theta)`

= tan θ