1.

If `theta=(17pi)/3` then, `tantheta-cottheta`= …A. `1/(2sqrt3)`B. `(-1)/(2sqrt3)`C. `2/(sqrt3)`D. `-(2)/(sqrt3)`

Answer» Correct Answer - D
We have, `theta=(17pi)/3`
`thereforetantheta-cottheta=tan((17pi)/3)-cot((17pi)/3))`
`=tan(5pi+(2pi)/3)-cot(5pi+(2pi)/3)`
`=tan(2pi)/3-cot(2pi)/3`
`=tan(pi-pi/3)-cot(pi-pi/3)`
`=-tanpi//3+cotpi//3`
`=-sqrt3+1/sqrt3)=(-3+1)/(sqrt3)=(-2)/(sqrt3)`


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