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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

2 sin (x) + 2

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1

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

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

2 sin^{2} (x) - 4 sin (x) - 6 = 0

cos^{2} (2 x) = \frac{1}{2} - \frac{1}{2} cos (2 x)

2 sin (A) - 3 = 0

3 sec (3 x) = 2

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

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