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

The general solution for 2-sin(x)=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=2pin,x=pi+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

2 cos^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 0

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = 2 πn, x = π + 2 πn

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

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

2 sec (x) = tan (x) + cot (x)

3 sin (2 x) = cos (2 x)

2 sin (6 x) + 3 = 0

What is the general solution for 2-sin(x)=2cos^2(x) ?
The general solution for 2-sin(x)=2cos^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=2pin,x=pi+2pin