How do you solve 3 cos 2x - 5 cos x = 1?Trigonometric Equation

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation 3*cos 2x - 5*cos x = 1 has to be solved.

`3*cos 2x - 5*cos x = 1`

=> `6*cos^2x - 3 - 5*cos x = 1`

=> `6*cos^2x - 5*cos x - 4 = 0`

=> `6*cos^2x - 8*cos x + 3*cos x - 4 = 0`

=> `2*cos x(3*cos x - 4) + 1(3*cos x - 4) = 0`

=> `(2*cos x + 1)(3*cos x - 4) = 0`

=> `cos x = -1/2` and `cos x = 4/3`

As cos x lies in the interval [-1, 1] ignore cos x = 4/3

cos x = -1/2

=> x = 120 and x = 240

The solution of the equation is 120 + n*360 and 240 + n*260 degrees.

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