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

The general solution for 3cos^2(x)-2cos(x)-2=0 is x=2.15146…+2pin,x=-2.15146…+2pin

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

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

x = 2.15146 \dots + 2 πn, x = - 2.15146 \dots + 2 πn

Solution steps

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

Solve by substitution

cos (x) = \frac{1 + 7}{3}, cos (x) = \frac{1 - 7}{3}

cos (x) = \frac{1 + 7}{3} :

No Solution

cos (x) = \frac{1 - 7}{3} : x = arccos (\frac{1 - 7}{3}) + 2 πn, x = - arccos (\frac{1 - 7}{3}) + 2 πn

Combine all the solutions

x = arccos (\frac{1 - 7}{3}) + 2 πn, x = - arccos (\frac{1 - 7}{3}) + 2 πn

Show solutions in decimal form

x = 2.15146 \dots + 2 πn, x = - 2.15146 \dots + 2 πn

5 sin (5 x) = 0

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

- 7 sin^{2} (θ) + 2 sin (θ) + 7 = 0

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

3 tan (2 x) + 3 = 0, 0 \leq x < 2 π

What is the general solution for 3cos^2(x)-2cos(x)-2=0 ?
The general solution for 3cos^2(x)-2cos(x)-2=0 is x=2.15146…+2pin,x=-2.15146…+2pin