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

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

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cos^2(x)=4(1+sin(x))

cos^{2} (x) = 4 (1 + sin (x))

x = \frac{3 π}{2} + 2 πn

Solution steps

cos^{2} (x) = 4 (1 + sin (x))

Subtract

4 (1 + sin (x))

from both sides

cos^{2} (x) - 4 (1 + sin (x)) = 0

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 3, sin (x) = - 1

sin (x) = - 3 :

No Solution

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

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

sin (x) + 2 = tan (x)

- 2 sin (\frac{θ}{2}) = 0

cos^{3} (θ) + cos^{2} (θ) - cos (θ) - 1 = 0

2 sin^{2} (x) - 2 sin (x) = 0

9 sin^{2} (x) - 6 sin (x) + 1 = 0

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