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

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

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

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

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

Solution steps

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

Subtract

sin (x)

from both sides

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

cos (x) = \frac{6}{7}

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

csc^{2} (x) = 2 csc (x)

cos (x) - 3 sin (x) = 0

2 cos (4 x) + 3 = 4 cos (2 x)

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