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

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

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

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

x = \frac{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{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

cos (2 π)

cos (β) = 0.8

cos (15 0^{\circ})

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

arcsin (\frac{3}{5})

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