What is the general solution for cos^2(x)-3cos(x)-2=0 ?

The general solution for cos^2(x)-3cos(x)-2=0 is x=2.16705…+2pin,x=-2.16705…+2pin

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cos^2(x)-3cos(x)-2=0

cos^{2} (x) - 3 cos (x) - 2 = 0

x = 2.16705 \dots + 2 πn, x = - 2.16705 \dots + 2 πn

Solution steps

cos^{2} (x) - 3 cos (x) - 2 = 0

Solve by substitution

cos (x) = \frac{3 + 17}{2}, cos (x) = \frac{3 - 17}{2}

cos (x) = \frac{3 + 17}{2} :

No Solution

cos (x) = \frac{3 - 17}{2} : x = arccos (\frac{3 - 17}{2}) + 2 πn, x = - arccos (\frac{3 - 17}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{3 - 17}{2}) + 2 πn, x = - arccos (\frac{3 - 17}{2}) + 2 πn

Show solutions in decimal form

x = 2.16705 \dots + 2 πn, x = - 2.16705 \dots + 2 πn

tan (4 x) = tan (2 x)

x, cos (2 x + 5 x) = cos (H x)

x, - 4 cos (x) - 4 cos (2 x) = 0

3 - 2 cos (x) = 3 - 2 sin (x)

3 sin (x) = sin (x) tan (x)

What is the general solution for cos^2(x)-3cos(x)-2=0 ?
The general solution for cos^2(x)-3cos(x)-2=0 is x=2.16705…+2pin,x=-2.16705…+2pin