How do you find the value of sin ((2pi)/3) Cos pi Tan ((2pi)/3)Cot ((5pi)/6)?

1 Answer
Apr 27, 2016

=>sin ((2pi)/3) Cos pi Tan ((2pi)/3)Cot ((5pi)/6)
=1/2 * -1 * -1/sqrt3*-1/sqrt3 =-1/6

Explanation:

cos pi = cos180 = -1

sin((2pi)/3)= sin 120 = sin (90 +30) = sin 30 = 1/2

Tan ((2pi)/3) = tan 120 = -tan 30 = -1/sqrt3

Cot ((5pi)/6) = cot 150 = - cot 60 = -tan(90-60)
= -tan30 =- 1/sqrt3

=>sin ((2pi)/3) Cos pi Tan ((2pi)/3)Cot ((5pi)/6)
=1/2 * -1 * -1/sqrt3*-1/sqrt3 =-1/6