Question

How do you solve `cos(x+pi/6)-1=cos(x-pi/6)`?

Answer 1

`x = (3pi)/2 + 2kpi`

Explanation:

Use the trig identiy:
cos (a + b) - cos (a - b) = - 2sin a.sin b
`cos (x + pi/6) - cos (x - pi/6) = 1` (1)
`- 2sin x.sin (pi/6) = 1`
`- 2sin x.(1/2) = 1`
`sin x = -1` -->
`x = (3pi)/2 + 2kpi.`
Check
`x = 3pi/2` --> `cos (x + pi/6) = cos ((10pi)/6) = cos ((5pi)/3) = 1/2`
`cos ((3pi)/2 - pi/6) = cos ((8pi)/6) = cos ((3pi)/4) = - 1/2`
(1) --> `1/2 - (-1/2) = 1.` OK