Question

How do you simplify `tan (-5pi / 6) - cot (7pi / 2)`?

Answer 1

Simplify trig expression.

Ans: `sqrt3/3`

Explanation:

`tan`(-5pi)/6`= tan (pi/6 - (6pi)/6) = tan (pi/6 - pi) = tan (pi/6) =`
`= sqrt3/3.`
`cot ((7pi)/2) = cot ((3pi)/2 + 2pi) = cot ((3pi)/2) = 0`, then
`tan ((-5pi)/6) - cot ((7pi)/2) = sqrt3 - 0 = sqrt3/3`