Question

How do you simplify `(csc theta cot theta) / sec theta`?

Answer 1

`(cscthetacottheta)/sectheta=cot^2theta`

Explanation:

As `csctheta=1/sintheta`, `cottheta=costheta/sintheta` and `sectheta=1/costheta`

Hence `(cscthetacottheta)/sectheta`

= `((1/sintheta)xx(costheta/sintheta))/(1/costheta`

= `(1/sintheta)xx(costheta/sintheta)xx(costheta/1)`

= `cos^2theta/sin^2theta`

= `cot^2theta`