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

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

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2cos^2(x)+2cos(x)-1=0

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

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

Solution steps

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

Solve by substitution

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

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

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

No Solution

Combine all the solutions

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

Show solutions in decimal form

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

2 sin^{2} (x) = 0

tan (x) = sin (x)

csc (x) = sec (x)

sec (x) = 3

- sin (x) = cos (x)

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