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

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

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3cos(θ)=2sin^2(θ)

3 cos (θ) = 2 sin^{2} (θ)

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

Solution steps

3 cos (θ) = 2 sin^{2} (θ)

Subtract

2 sin^{2} (θ)

from both sides

3 cos (θ) - 2 sin^{2} (θ) = 0

Rewrite using trig identities

- (1 - cos^{2} (θ)) \cdot 2 + 3 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 2

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

cos (θ) = - 2 :

No Solution

Combine all the solutions

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

sin (x) - sin (x) cos (x) = 0

\frac{6}{3} cos (x) = \frac{1}{2}

2 sin^{2} (θ) = - 3 sin (θ) - 1

sin (x) = 1.9 cos (x)

tan^{2} (x) + 9 tan (x) + 1 = 0

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