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If theta=(17pi)/3 then, tantheta-cotthet...

If `theta=(17pi)/3` then, `tantheta-cottheta`= …

A

`1/(2sqrt3)`

B

`(-1)/(2sqrt3)`

C

`2/(sqrt3)`

D

`-(2)/(sqrt3)`

Text Solution

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The correct Answer is:
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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