Question

If θ = `(17π)/3` then, tan θ – cot θ = ______.

पर्याय

• `1/(2sqrt3)`

• `(-1)/(2sqrt3)`

• `2/sqrt3`

• `-2/sqrt3`

Answer 1

If θ = `(17π)/3` then, tan θ – cot θ = `underlinebb(-2/sqrt3)`.

Explanation:

We have, `theta = (17π)/3`

∴ tan θ – cot θ = `tan ((17π)/3) - cot ((17π)/3)`

= `tan (5π + (2π)/3) - cot (5π + (2π)/3)`

= `tan  (2π)/3 - cot  (2π)/3`

= `tan (π - π/3) - cot (π - π/3)`

= `- tan  π/3 + cot  π/3`

= `- sqrt3 + 1/sqrt3`

= `(- 3 + 1)/sqrt3`

= `(-2)/sqrt3`