What is the general solution for cos(θ)(1+cos(θ))=sin^2(θ) ?

The general solution for cos(θ)(1+cos(θ))=sin^2(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin

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cos(θ)(1+cos(θ))=sin^2(θ)

cos (θ) (1 + cos (θ)) = sin^{2} (θ)

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

Solution steps

cos (θ) (1 + cos (θ)) = sin^{2} (θ)

Subtract

sin^{2} (θ)

from both sides

cos (θ) (1 + cos (θ)) - sin^{2} (θ) = 0

Rewrite using trig identities

- 1 + cos (θ) + 2 cos^{2} (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 = π + 2 πn

Combine all the solutions

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

cos (θ) = - 0.8, sin (π^{2} - θ)

0 = a (1 + cos (2 θ))

4 sin (2 x) = 3 cos (x)

sin (b) = (\frac{250 km}{590 km}) sin (2 3^{\circ}), 8 2^{\circ}

sin (x) = \frac{30}{60}

What is the general solution for cos(θ)(1+cos(θ))=sin^2(θ) ?
The general solution for cos(θ)(1+cos(θ))=sin^2(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin