Question

How do you verify `tan(theta)/cot(theta)=tan^2(theta)`?

Answer 1

Use the definition of `cot(theta)` as the inverse of `tan(theta)`
and the fact that dividing by `1/x` is the same as multiplying by `x`

Explanation:

`(tan(theta))/(cot(theta))`

`color(white)("XXX")=tan(theta) div cot(theta)`

`color(white)("XXX")=tan(theta) div 1/(tan(theta))` [by definition of `cot(theta)`]

`color(white)("XXX")=tan(theta)xxtan(theta)` [since `axx1/x <=> axxx`]

`color(white)("XXX")=tan^2(theta)`