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

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

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2sin^2(θ)+3cos(θ)=3

2 sin^{2} (θ) + 3 cos (θ) = 3

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

Solution steps

2 sin^{2} (θ) + 3 cos (θ) = 3

Subtract

3

from both sides

2 sin^{2} (θ) + 3 cos (θ) - 3 = 0

Rewrite using trig identities

- 1 - 2 cos^{2} (θ) + 3 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = 1

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

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

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

2 sin (θ) = 1

sin (2 x) (csc (2 x) - 2) = 0

tan (x - π) + 2 sin (x - π) = 0

tan (4 5^{\circ}) = \frac{1 - cos ( u )}{sin ( u )}

1 - 2 cos^{2} (x) = 0

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