Question

If 3 tan θ = 4, find the value of `(4cos theta - sin theta)/(2cos theta + sin theta)`

Answer 1

3 tan theta = 4 find `(4cos theta - sin theta)/(2cos theta + sin theta)` ....(i)

`tan theta = 4/3`

Dividing equation (i) with cos θ we get

`= ((4cos theta - sin theta)/cos theta)/((2 cos theta + sin theta)/cos theta) = (4 - tan theta)/(2 + tan theta)   [∵ sin theta/cos theta = tan theta]`

`= (4 - tan theta)/(2 + tan theta)     [∵ sin theta/cos theta = tan theta]`

`= (4 - 4/1)/(2 + 4/5)`

`= (12 - 4)/(6 + 4)`

`= 8/10`

`= 4/5`