1.

If `4 tantheta=3,` then `((4sintheta-costheta)/(4 sintheta+costheta))` is equal toA. `2/3`B. `1/3`C. `1/2`D. `3/4`

Answer» Correct Answer - C
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)]`


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