What is the general solution for cos(2x)=0.5 ?

The general solution for cos(2x)=0.5 is x= pi/6+pin,x=(5pi)/6+pin

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cos(2x)=0.5

cos (2 x) = 0.5

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

Solution steps

cos (2 x) = 0.5

General solutions for

cos (2 x) = 0.5

2 x = \frac{π}{3} + 2 πn, 2 x = \frac{5 π}{3} + 2 πn

Solve

2 x = \frac{π}{3} + 2 πn : x = \frac{π}{6} + πn

Solve

2 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{6} + πn

x = \frac{π}{6} + πn, x = \frac{5 π}{6} + πn

cos^{2} (x) = - 1

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

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

(sin (x) + cos (x))^{2} = sin^{2} (x) + cos^{2} (x)

cos (2 x) + 3 sin (x) + 1 = 0

What is the general solution for cos(2x)=0.5 ?
The general solution for cos(2x)=0.5 is x= pi/6+pin,x=(5pi)/6+pin