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

The general solution for cos^2(x)+2cos(x)-1=0 is x=1.14371…+2pin,x=2pi-1.14371…+2pin

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

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

x = 1.14371 \dots + 2 πn, x = 2 π - 1.14371 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = - 1 + 2, cos (x) = - 1 - 2

cos (x) = - 1 + 2 : x = arccos (- 1 + 2) + 2 πn, x = 2 π - arccos (- 1 + 2) + 2 πn

cos (x) = - 1 - 2 :

No Solution

Combine all the solutions

x = arccos (- 1 + 2) + 2 πn, x = 2 π - arccos (- 1 + 2) + 2 πn

Show solutions in decimal form

x = 1.14371 \dots + 2 πn, x = 2 π - 1.14371 \dots + 2 πn

tan (θ) = 0.1

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

8 sin^{2} (θ) = 6

72 sin^{2} (x) = 72 - 36 cos (x)

3 cos^{2} (x) - 4 cos (x) + 1 = 0

What is the general solution for cos^2(x)+2cos(x)-1=0 ?
The general solution for cos^2(x)+2cos(x)-1=0 is x=1.14371…+2pin,x=2pi-1.14371…+2pin