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

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

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sqrt(3)sin(2x)+cos(2x)=2cos(2x)

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

x = \frac{π}{12} + \frac{πn}{2}

Solution steps

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

Subtract

2 cos (2 x)

from both sides

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

Rewrite using trig identities

3 tan (2 x) - 1 = 0

Move

1

to the right side

3 tan (2 x) = 1

Divide both sides by

3

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

General solutions for

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

2 x = \frac{π}{6} + πn

Solve

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

x = \frac{π}{12} + \frac{πn}{2}

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

tan^{2} (\frac{x}{2}) = 1

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

1 - sin (x - \frac{3 π}{2}) = - sin (x - \frac{π}{2})

sin (x + \frac{π}{2}) = \frac{3}{2}

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