If ` theta ` in the first quadrant and ` 5 tan theta =4 " then " ( 5 sin theta - 3 sin theta)/( sin theta + 2 cos theta)` is equal to

Options

A. `5/14`
B. `3/14`
C. `1/14`
D. 0

Answer

A

Explanation

Given ` tan theta = 4/5`
Consider, ` ( 5 sin theta -3 cos theta)/(sin theta + 2 cos theta) = ( 5 sin theta - 3 cos theta)/( sin theta + 2 cos theta) = ( 5 tan theta -3)/( tan theta -2) `
Dividing `N^( r) and D^( r) ` by cos x)
`(5 (4/5)-3)/(4/5+2) = 1/((14/5))=5/14`