What is the general solution for 2sin^2(x)-1=cos(x) ?

The general solution for 2sin^2(x)-1=cos(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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2sin^2(x)-1=cos(x)

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

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

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

Subtract

cos (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

9 sin^{2} (θ) + 19 sin (θ) + 8 = 7 sin (θ) + 4

arccos (x) = \frac{7 π}{8}

\frac{sin ( 3 7 ^{\circ} )}{23} = \frac{sin ( x )}{21}

csc (x) = \frac{1}{3}

(cot (x) + 1) (3 tan (x) - 1) = 0

What is the general solution for 2sin^2(x)-1=cos(x) ?
The general solution for 2sin^2(x)-1=cos(x) is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin