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

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

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

3 sin (x) = 3 \cdot sin (x) + 3 cos (x) + 3 sin (x)

x = \frac{2 π}{3} + πn

Solution steps

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

Subtract

3 sin (x) + 3 cos (x) + 3 sin (x)

from both sides

- 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

csc (θ) + 1 = 0, (0, 2 π)

x, y^{2} = - 2 tan (2 x)

2 cos^{2} (a) - 3 cos (a) + 1 = 0

sin (x) \cdot cos (2 x) = 0.5 - sin (2 x) \cdot cos (x)

tan (x) = 0.625

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