Question

How do you find the exact value of Cot π/3 - cosπ/6?

Answer 1

This evaluates to `-1/sqrt(3)`

Explanation:

We can rewrite `cotx` as `cosx/sinx`.

`=cos(pi/3)/sin(pi/3) - cos(pi/6)`

We can now easily evaluate using our knowledge of the 30-60-90 triangle.

`= (1/2)/(sqrt(3)/2) - sqrt(3)/2`

`= 1/sqrt(3) - sqrt(3)/2`

`= (1 - 3)/(2sqrt(3))`

`= -1/sqrt(3)`

Hopefully this helps!