What is the general solution for pi/6 =cos(2x) ?

The general solution for pi/6 =cos(2x) is x=(1.01972…)/2+pin,x=pi-(1.01972…)/2+pin

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pi/6 =cos(2x)

\frac{π}{6} = cos (2 x)

x = \frac{1.01972 \dots}{2} + πn, x = π - \frac{1.01972 \dots}{2} + πn

Solution steps

\frac{π}{6} = cos (2 x)

Switch sides

cos (2 x) = \frac{π}{6}

Apply trig inverse properties

2 x = arccos (\frac{π}{6}) + 2 πn, 2 x = 2 π - arccos (\frac{π}{6}) + 2 πn

Solve

2 x = arccos (\frac{π}{6}) + 2 πn : x = \frac{arccos ( \frac{π}{6} )}{2} + πn

Solve

2 x = 2 π - arccos (\frac{π}{6}) + 2 πn : x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

x = \frac{arccos ( \frac{π}{6} )}{2} + πn, x = π - \frac{arccos ( \frac{π}{6} )}{2} + πn

Show solutions in decimal form

x = \frac{1.01972 \dots}{2} + πn, x = π - \frac{1.01972 \dots}{2} + πn

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tan (x) + 5 = \frac{15 - 3}{3}

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

What is the general solution for pi/6 =cos(2x) ?
The general solution for pi/6 =cos(2x) is x=(1.01972…)/2+pin,x=pi-(1.01972…)/2+pin