If `3tantheta+4=0, "where"(pi//2)ltthetaltpi`, then what is the value of `2cottheta-5costheta+sintheta`?

Options

A. `-(53)/(10)`
B. `(7)/(10)`
C. `(23)/(10)`
D. `(37)/(10)`

Answer

C

Explanation

As given , 3 `tantheta+4=0rArrtantheta=-(4)/(3)`
`[theta"lies in second quadrant" i.e ., (pi)/(2)ltthetaltpi]`
`thereforecot=-(3)/(4)rArrcostheta=-(3)/(5)andsintheta=(4)/(5)`
Now , 2 `cottheta-5costheta+sintheta`
`=-(6)/(4)+(15)/(5)+(4)/(5)=(-30+60+16)/(20)=(23)/(10)`