What is the general solution for cos(2x)= 1/3 ?

The general solution for cos(2x)= 1/3 is x=(1.23095…)/2+pin,x=pi-(1.23095…)/2+pin

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cos(2x)= 1/3

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

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

Solution steps

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{1.23095 \dots}{2} + πn, x = π - \frac{1.23095 \dots}{2} + πn

2 sin^{2} (x) - 5 sin (x) + 3 = 0

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

4 cos (x) tan (x) - 3 tan (x) = 0

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

sin (x) = 2 cos (x)

What is the general solution for cos(2x)= 1/3 ?
The general solution for cos(2x)= 1/3 is x=(1.23095…)/2+pin,x=pi-(1.23095…)/2+pin