If A lies in the second quadrant and `3tanA + 4=0`, then find the value of `2cotA-5cosA+ sinA`.

Options

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

Answer

B

Explanation

Given equation, `" "3tanA +4=0`
`rArr" "3tanA =-4`
`rArr" "tanA=(-4)/(3)`
`rArr" "cotA=(-3)/(4)`
`rArr" "secA =sqrt(1+(16)/(9))=sqrt((25)/(9))=pm(5)/(3)`
`rArr" "secA =(-5)/(3)" "` [since, A lies in second quadrant]
`" "cosA =(-3)/(5)`
`" "sinA =sqrt(1-(9)/(25))=(sqrt(25-9))/(25)=pm(4)/(5)`
`" "sinA =(4)/(5) " "` [since, A lies in second quadrant]
`therefore" "2cotA -5cosA +sinA =2((-3)/(4))-5((-3)/(5))+(4)/(5)`
`" "=(-6)/(4)+3+(4)/(5)`
`" "=(-30+60+16)/(20)=(46)/(20)`
`" "=(23)/(10)`