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

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

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3sin(θ)=sqrt(3)sin(θ)+3cos(θ)+3sin(θ)

3 sin (θ) = 3 sin (θ) + 3 cos (θ) + 3 sin (θ)

θ = \frac{2 π}{3} + πn

Solution steps

3 sin (θ) = 3 sin (θ) + 3 cos (θ) + 3 sin (θ)

Subtract

3 sin (θ) + 3 cos (θ) + 3 sin (θ)

from both sides

- 3 sin (θ) - 3 cos (θ) = 0

Rewrite using trig identities

- 3 tan (θ) - 3 = 0

Move

3

to the right side

- 3 tan (θ) = 3

Divide both sides by

- 3

tan (θ) = - 3

General solutions for

tan (θ) = - 3

θ = \frac{2 π}{3} + πn

2 sin^{2} (x) - 3 sin (x) = 2

tan (x + π) + 2 sin (x + π) = 0, 0 \leq x \leq 2 π

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

22 cos (θ) + 3 = 5

sin (a) cos (a) = 1

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