Question

How do i solve 2cos 2x -1+0 ?

Can someone please explain how to do this for me? It would be greatly appreciated! :)

Answer 1

General solution:
`x= pi/6+pin`
`x= (5pi)/6+pin`
n is an element of all integers

Explanation:

`2cos 2x -1=0`

Cos double angle identity:
`cos2x= 2cos^2x-1`

Substitute:
`2(2cos^2x-1) -1=0`
`4cos^2x-3=0`
`cos^2x=3/4`
`cosx= +-sqrt3/2`
`x= pi/6, (5pi)/6, (7pi)/6, (11pi)/6`

General solution:
`x= pi/6+pin`
`x= (5pi)/6+pin`
n is an element of all integers