What is the general solution for 6sin(θ)+sqrt(3)sin(θ)tan(θ)=3sin(θ) ?

The general solution for 6sin(θ)+sqrt(3)sin(θ)tan(θ)=3sin(θ) is θ=2pin,θ=pi+2pin,θ=(2pi)/3+pin

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6sin(θ)+sqrt(3)sin(θ)tan(θ)=3sin(θ)

6 sin (θ) + 3 sin (θ) tan (θ) = 3 sin (θ)

θ = 2 πn, θ = π + 2 πn, θ = \frac{2 π}{3} + πn

Solution steps

6 sin (θ) + 3 sin (θ) tan (θ) = 3 sin (θ)

Subtract

3 sin (θ)

from both sides

3 sin (θ) + 3 sin (θ) tan (θ) = 0

Factor

3 sin (θ) + 3 sin (θ) tan (θ) : sin (θ) (3 + 3 tan (θ))

sin (θ) (3 + 3 tan (θ)) = 0

Solving each part separately

sin (θ) = 0 or 3 + 3 tan (θ) = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

3 + 3 tan (θ) = 0 : θ = \frac{2 π}{3} + πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{2 π}{3} + πn

cos (2 x) sin (x) = 1

sin (θ) = 10

17. 6^{2} = 1 5^{2} + 13. 1^{2} - 2 (15) (13.1) \cdot cos (A)

x, f = cos (\frac{1}{x ^{2}})

sin (θ) = 45

What is the general solution for 6sin(θ)+sqrt(3)sin(θ)tan(θ)=3sin(θ) ?
The general solution for 6sin(θ)+sqrt(3)sin(θ)tan(θ)=3sin(θ) is θ=2pin,θ=pi+2pin,θ=(2pi)/3+pin