Question

If `tan theta = a/b`, find the value of `(cos theta + sin theta)/(cos theta - sin theta)`

Answer 1

`tan theta = a/b` find `(cos theta + sin theta)/(cos theta - sin theta)`  ....(i)

Divide equation (i) with cos θ, we get

`=> ((cos theta + sin theta)/cos theta)/((cos theta - sin theta)/cos theta)`

`=> (1 + sin theta/cos theta)/(1 - sin theta/cos theta)`

`=> (1 + tan theta)/(1 - tan theta)`

`= (1+ a/b)/(1 - a/b)`

`= (b + a)/(b - a)`