What is the general solution for 6sin(θ)=6sin(2θ) ?

The general solution for 6sin(θ)=6sin(2θ) is θ=2pin,θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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6sin(θ)=6sin(2θ)

6 sin (θ) = 6 sin (2 θ)

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

6 sin (θ) = 6 sin (2 θ)

Subtract

6 sin (2 θ)

from both sides

6 sin (θ) - 6 sin (2 θ) = 0

Rewrite using trig identities

6 sin (θ) - 12 cos (θ) sin (θ) = 0

Factor

6 sin (θ) - 12 cos (θ) sin (θ) : - 6 sin (θ) (2 cos (θ) - 1)

- 6 sin (θ) (2 cos (θ) - 1) = 0

Solving each part separately

sin (θ) = 0 or 2 cos (θ) - 1 = 0

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

2 cos (θ) - 1 = 0 : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = π + 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

2 sin (1 5^{\circ}) cos (1 5^{\circ}) = tan (x)

6 sin^{2} (x) + 5 cos (x) = 7

3 cos (x) + sin (x) = - 1

- 3 = tan^{2} (θ) - 2 - 2 tan (θ)

- 2 cos^{2} (x) - 9 sin (x) - 3 = 0

What is the general solution for 6sin(θ)=6sin(2θ) ?
The general solution for 6sin(θ)=6sin(2θ) is θ=2pin,θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin