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

The general solution for 2cos(2x)=sqrt(3) is x= pi/(12)+pin,x=(11pi)/(12)+pin

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2cos(2x)=sqrt(3)

2 cos (2 x) = 3

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

Solution steps

2 cos (2 x) = 3

Divide both sides by

2

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

General solutions for

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

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{11 π}{6} + 2 πn

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{11 π}{12} + πn

cos (2 x) = 1 + 4 sin (x)

(tan (θ) + 1) (cos (θ) - 1) = 0

sin (5 x) = sin (3 x)

sin (x + π) - sin (x) + 1 = 0

sin (x) = 3 - sin (x)

What is the general solution for 2cos(2x)=sqrt(3) ?
The general solution for 2cos(2x)=sqrt(3) is x= pi/(12)+pin,x=(11pi)/(12)+pin