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

The general solution for sin(2x)-sqrt(3)cos(2x)=0 is x= pi/6+(pin)/2

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

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

x = \frac{π}{6} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

tan (2 x) - 3 = 0

Move

3

to the right side

tan (2 x) = 3

General solutions for

tan (2 x) = 3

2 x = \frac{π}{3} + πn

Solve

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

x = \frac{π}{6} + \frac{πn}{2}

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

4 sec (x) + 8 = 0

x, ln (y) = e^{y} sin (x)

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

tan (x) sin (2 x) = 0

What is the general solution for sin(2x)-sqrt(3)cos(2x)=0 ?
The general solution for sin(2x)-sqrt(3)cos(2x)=0 is x= pi/6+(pin)/2