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

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

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sin(2θ)+3cos(θ)=cos(θ)

sin (2 θ) + 3 cos (θ) = cos (θ)

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

Solution steps

sin (2 θ) + 3 cos (θ) = cos (θ)

Subtract

cos (θ)

from both sides

sin (2 θ) + 2 cos (θ) = 0

Rewrite using trig identities

2 cos (θ) + 2 cos (θ) sin (θ) = 0

Factor

2 cos (θ) + 2 cos (θ) sin (θ) : 2 cos (θ) (sin (θ) + 1)

2 cos (θ) (sin (θ) + 1) = 0

Solving each part separately

cos (θ) = 0 or sin (θ) + 1 = 0

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

sin (θ) + 1 = 0 : θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

1 + cos (θ) = 1 + sin (θ)

500 = 538 cos (x - 1 0^{\circ})

0 = sec^{2} (x) e^{t a n (x)} (2 tan (x) + sec^{2} (x))

tan (x) = 3, - 18 0^{\circ} < x < 18 0^{\circ}

cot^{2} (t) csc (t) = sin (t)

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