If `5 cot theta = 3 ," find the value of "((5sin theta - 3 cos theta )/(4 sin theta + 3 cos theta)).`

Options

A. `(11)/(29)`
B. `(16)/(19)`
C. `(16)/(29)`
D. `(34)/(29)`

Answer

C

Explanation

`5 cot theta =3implies cot theta =(3)/(5) .`
Given expression `=((5sin theta - 3 cos theta )/(4 sin theta+3cos theta ))=((5-3 cot theta))/((4+ 3 cot theta ))`
`["dividing num.and denom, by "sin theta ]`
`=((5-3xx(3)/(5)))/((4+3xx(3)/(5)))=((5-(9)/(5)))/((4+(9)/(5)))=((16)/(5)xx(5)/(29))=(16)/(29).`