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

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

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

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

x = \frac{2 π}{3} + πn

Solution steps

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

Rewrite using trig identities

3 tan (x) + 3 = 0

Move

3

to the right side

3 tan (x) = - 3

Divide both sides by

3

tan (x) = - 3

General solutions for

tan (x) = - 3

x = \frac{2 π}{3} + πn

4 sin (2 x) + 4 cos (x) = 0

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

2 cos (x) = tan (x) + sec (x)

sin^{2} (x) cos (x) = \frac{2}{3 π}

tan (φ) = - \frac{1}{6}

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