What is the general solution for 2+3cos^2(θ)=sin^2(θ)+4cos(θ) ?

The general solution for 2+3cos^2(θ)=sin^2(θ)+4cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin

Popular >

2+3cos^2(θ)=sin^2(θ)+4cos(θ)

2 + 3 cos^{2} (θ) = sin^{2} (θ) + 4 cos (θ)

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

Solution steps

2 + 3 cos^{2} (θ) = sin^{2} (θ) + 4 cos (θ)

Subtract

sin^{2} (θ) + 4 cos (θ)

from both sides

2 + 3 cos^{2} (θ) - sin^{2} (θ) - 4 cos (θ) = 0

Rewrite using trig identities

1 - 4 cos (θ) + 4 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}

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

Combine all the solutions

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

arctan (4 x) + arctan (6 x) = \frac{π}{2}

x, y = \frac{1}{tan ( x \cdot π )}

cos (x) = sin (\frac{7 π}{6})

100 = 100 + 30 sin (\frac{12 π}{5} t)

\frac{10}{sin ( x )} = \frac{100}{sin ( 9 0 ^{\circ} )}

What is the general solution for 2+3cos^2(θ)=sin^2(θ)+4cos(θ) ?
The general solution for 2+3cos^2(θ)=sin^2(θ)+4cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin