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

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

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

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

x = \frac{π}{3} + \frac{πn}{2}

Solution steps

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

Rewrite using trig identities

3 + tan (2 x) = 0

Move

3

to the right side

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}

cos (\frac{- π}{2} + \frac{x}{2}) = 0

cos (x) = - 0.175

sec^{2} (x) = 2 tan^{2} (x)

\frac{sin ( x )}{cos ( x )} - 5 + \frac{4 cos ( x )}{sin ( x )} = 0

x, y = sin (3.2 x)

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