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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

2 + 2 sin (x)

from both sides

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

arccsc (\frac{2 3}{3})

csc (θ) + 2 = 0

csc (x) = 2

cos (\frac{5 π}{6})

tan (- 1)

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