What is the general solution for solvefor x,1-2cos^2(x)-2cos(x)=0 ?

The general solution for solvefor x,1-2cos^2(x)-2cos(x)=0 is x=1.19606…+2pin,x=2pi-1.19606…+2pin

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solvefor x,1-2cos^2(x)-2cos(x)=0

solve for

x, 1 - 2 cos^{2} (x) - 2 cos (x) = 0

x = 1.19606 \dots + 2 πn, x = 2 π - 1.19606 \dots + 2 πn

Solution steps

1 - 2 cos^{2} (x) - 2 cos (x) = 0

Solve by substitution

cos (x) = - \frac{1 + 3}{2}, cos (x) = \frac{3 - 1}{2}

cos (x) = - \frac{1 + 3}{2} :

No Solution

cos (x) = \frac{3 - 1}{2} : x = arccos (\frac{3 - 1}{2}) + 2 πn, x = 2 π - arccos (\frac{3 - 1}{2}) + 2 πn

Combine all the solutions

x = arccos (\frac{3 - 1}{2}) + 2 πn, x = 2 π - arccos (\frac{3 - 1}{2}) + 2 πn

Show solutions in decimal form

x = 1.19606 \dots + 2 πn, x = 2 π - 1.19606 \dots + 2 πn

1 = tan (\frac{x}{3})

cos (12 x) = 0

cos (2 x + 1) = \frac{1}{2}

2 ∣ sin (4 x) ∣ = 0

sin (α) = - \frac{3}{5}

What is the general solution for solvefor x,1-2cos^2(x)-2cos(x)=0 ?
The general solution for solvefor x,1-2cos^2(x)-2cos(x)=0 is x=1.19606…+2pin,x=2pi-1.19606…+2pin