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 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

2 cos^{2} (x) + 5 sin (x) - 4 = 0

2 cos^{2} (x) - 3 cos (x) = 0

cos^{2} (\frac{x}{2}) - sin^{2} (\frac{x}{2}) = sin (x)

tan (x) + sec (x) = - 1

2 sin^{2} (θ) - cos (θ) - 1 = 0

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