If `cottheta=(24)/(7)" and "theta` is not in the first quadrant, then find the value of `tantheta-sectheta`

Options

A. 1
B. `(4)/(3)`
C. `(3)/(2)`
D. `(5)/(4)`

Answer

B

Explanation

Given, `thereforesintheta=(1)/(2)rArrtheta=30^(@)`
As `cottheta=(24)/(7)``tantheta " is positive and " thetanotinQ_(1)`,

`theta notinQ_(3)*`
`thereforesectheta=-(25)/(24)`
`tantheta=(7)/(24)`
Now `tantheta-sectheta=(7)/(24)+(25)/(24)`
`=(32)/(24)=(4)/(3)`