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=1.94553…+2pin,x=-1.94553…+2pin

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

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

x = 1.94553 \dots + 2 πn, x = - 1.94553 \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} :

No Solution

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

Combine all the solutions

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

Show solutions in decimal form

x = 1.94553 \dots + 2 πn, x = - 1.94553 \dots + 2 πn

sin (b) = \frac{1}{3}

35 + 53 sin (2 T - 31.9) = 0

cos (2 x) = - 12

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

sin (θ) = - \frac{5}{6}, sec (θ)

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=1.94553…+2pin,x=-1.94553…+2pin