If `4 tantheta=3,` then `((4sintheta-costheta)/(4 sintheta+costheta))` is equal to

Options

A. `2/3`
B. `1/3`
C. `1/2`
D. `3/4`

Answer

C

Explanation

Given, 4tan`theta=3`
`rArr tantheta=3/4`
`therefore (4sintheta-costheta)/(4sintheta-costheta) = (4(sintheta)/(costheta)-1)/(4(sintheta)/(costheta)+1)`
[divide by cos`theta` in both numerator and denominator]
`(4tantheta-1)/(4tantheta+1)` `[therefore tantheta=(sintheta)/(costheta)]`
`=(4(3//4)-1)/(4(3//4)+1)=(3-1)/(3+1)=2/4=1/2` [put the value from Eq. 9i)]`