Question

If 3 cot θ = 2, find the value of  `(4sin theta - 3 cos theta)/(2 sin theta + 6cos theta)`.

Answer 1

`cot theta = 2/3`

`= ((4 sin theta - 3 cos theta)/sin theta)/((2sin theta + 6 cos theta)/sin theta)`

`= (4 - 3 cot theta)/(2 + 6 cot theta)`

`= (4 - 3 xx 2/3)/(2 + 6 xx 2/3)`

`= (4 + 2)/(2 + 4) = 2/6`

`= 1/3`