If `theta=(17pi)/(3)` then, `tan theta- cot theta` = . . .

Options

A. `(1)/(2sqrt(3))`
B. `(-1)/(2sqrt(3))`
C. `(2)/(sqrt(3))`
D. `-(2)/(sqrt(3))`

Answer

D

Explanation

We have, `theta=(17pi)/(3)`
`therefore theta-cot theta=tan((17pi)/(3))-cot((17pi)/(3))`
`=tan(5pi+(2pi)/(3))-cot(5pi+(2pi)/(3))`
`="tan"(5pi+(2pi)/(3))-cot(5pi+(2pi)/(3))`
`="tan"(2pi)/(3)-"cot"(2pi)/(3)`
`="tan"(2pi)/(3)-"cot"(2pi)/(3)`
`="tan"(pi-(pi)/(3))-cot(pi-(pi)/(3))`
`=-tanpi//3+cot pi//3`
`=-sqrt(3)+(1)/(sqrt(3))=(-3+1)/(sqrt(3))=(-2)/(sqrt(3))`