Solve the equation 6cos^2x-3cosx-2cosx+1=0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation `6cos^2x-3cosx-2cosx+1=0` has to be solved for x.

`6cos^2x-3cosx-2cosx+1=0`

=> `6cos^2x-5cosx+1=0`

Let cos x = y

=> `6y^2 - 5y + 1 = 0`

=> `6y^2 - 3y - 2y + 1 = 0`

=> `3y(2y - 1) - 1(2y - 1) = 0`

=> (3y - 1)(2y - 1) = 0

=> y = 1/3 and y = 1/2

cos x = 1/3 and cos x = 1/2

x= `cos^-1(1/3)` and x = `cos^-1(1/2)`

The solution to the given equation is `x= cos^-1(1/3)` and `x = cos^-1(1/2)`

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