Question

How do you find the value of `cot 60` using the double angle or half angle identity?

Answer 1

`sqrt3/3`

Explanation:

Use the trig identity:
`tan 2a = (2tan a)/(1 - tan^2 a)`
`cot 2a = 1/(tan 2a) = (1 - tan^2 a)/(2tan a)`
Substitute in the equation a = 30 and 2a = 60, we get:
`cot 60 = (1 - tan^2 30)/(2tan (30)`
Trig table -->
`cot 60 = ((1 - 1/3))/((2sqrt3)/3) =2/(2sqrt3) = 1/sqrt3 = sqrt3/3`