What is the general solution for 3-3sin(θ)=6cos^2(θ) ?

The general solution for 3-3sin(θ)=6cos^2(θ) is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin

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3-3sin(θ)=6cos^2(θ)

3 - 3 sin (θ) = 6 cos^{2} (θ)

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Solution steps

3 - 3 sin (θ) = 6 cos^{2} (θ)

Subtract

6 cos^{2} (θ)

from both sides

3 - 3 sin (θ) - 6 cos^{2} (θ) = 0

Rewrite using trig identities

- 3 - 3 sin (θ) + 6 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = 1, sin (θ) = - \frac{1}{2}

sin (θ) = 1 : θ = \frac{π}{2} + 2 πn

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

Combine all the solutions

θ = \frac{π}{2} + 2 πn, θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sin (x) + sin^{2} (x) + cos^{2} (x) = 1

tan (3 x) = 5 tan (x)

2 cos (2 x) - 2 = 0

3 tan^{2} (x) + 4 sec (x) = - 4

tan (x + 2 0^{\circ}) \cdot tan (x - 2 0^{\circ}) = 1

What is the general solution for 3-3sin(θ)=6cos^2(θ) ?
The general solution for 3-3sin(θ)=6cos^2(θ) is θ= pi/2+2pin,θ=(7pi)/6+2pin,θ=(11pi)/6+2pin