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

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lemong | Student, Undergraduate | Honors

Posted August 22, 2012 at 2:47 PM via web

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

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted August 22, 2012 at 2:58 PM (Answer #1)

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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` }

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