What is the general solution for sqrt(3)sin(2x)+3cos(2x)=0 ?

The general solution for sqrt(3)sin(2x)+3cos(2x)=0 is x= pi/3+(pin)/2

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

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

x = \frac{π}{3} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

3 tan (2 x) + 3 = 0

Move

3

to the right side

3 tan (2 x) = - 3

Divide both sides by

3

tan (2 x) = - 3

General solutions for

tan (2 x) = - 3

2 x = \frac{2 π}{3} + πn

Solve

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

x = \frac{π}{3} + \frac{πn}{2}

3 cos (θ) = 2 sin^{2} (θ)

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

\frac{6}{3} cos (x) = \frac{1}{2}

2 sin^{2} (θ) = - 3 sin (θ) - 1

sin (x) = 1.9 cos (x)

What is the general solution for sqrt(3)sin(2x)+3cos(2x)=0 ?
The general solution for sqrt(3)sin(2x)+3cos(2x)=0 is x= pi/3+(pin)/2