What is the general solution for 4(1+sin(θ))=cos^2(θ) ?

The general solution for 4(1+sin(θ))=cos^2(θ) is θ=(3pi)/2+2pin

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4(1+sin(θ))=cos^2(θ)

4 (1 + sin (θ)) = cos^{2} (θ)

θ = \frac{3 π}{2} + 2 πn

Solution steps

4 (1 + sin (θ)) = cos^{2} (θ)

Subtract

cos^{2} (θ)

from both sides

4 (1 + sin (θ)) - cos^{2} (θ) = 0

Rewrite using trig identities

3 + sin^{2} (θ) + 4 sin (θ) = 0

Solve by substitution

sin (θ) = - 1, sin (θ) = - 3

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

sin (θ) = - 3 :

No Solution

Combine all the solutions

θ = \frac{3 π}{2} + 2 πn

4 csc (θ) + 4 = 0

4 cos^{2} (4 x) - 3 = 0

tan^{2} (x) = cot (x)

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

tan^{2} (θ) = 0

What is the general solution for 4(1+sin(θ))=cos^2(θ) ?
The general solution for 4(1+sin(θ))=cos^2(θ) is θ=(3pi)/2+2pin