Solve for x:`(sqrt(1-cos x))^(1+cos 2x+2 cos x)=1`

### 1 Answer | Add Yours

The equation `(sqrt(1-cos x))^(1+cos 2x+2 cos x)=1` has to be solved for x.

`(sqrt(1-cos x))^(1+cos 2x+2 cos x)=1` if `1+cos 2x+2 cos x = 0` or if `sqrt(1 - cos x) = 1`

`1+cos 2x+2 cos x = 0`

=> `1 + 2*cos^2x - 1 + 2*cos x = 0`

=> `2*cos^2x + 2*cos x = 0`

=> `cos x(cos x + 1) = 0`

=> `cos x = 0` and `cos x = -1`

=> `x = pi/2` , `x = 3*pi/2` and `x = pi`

`sqrt(1 - cos x) = 1`

=> `1 - cos x = 1`

=> `cos x = 1`

=> `x = 0 `

**The general solution of the equation is {`2*n*pi` , `pi/2 + 2*n*pi` , `3*pi/2+2*n*pi` and `pi + 2*n*pi` }**

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes