What is the general solution for sin^2(x)-cos^2(x)+cos(x)=0 ?

The general solution for sin^2(x)-cos^2(x)+cos(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin

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sin^2(x)-cos^2(x)+cos(x)=0

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

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = 2 πn

8 cos (x) - 42 = 0

3 csc (x) - 23 = 0

x, arccos (x) = \frac{1}{2}

cos (2 x) = \frac{1}{5}

sin^{2} (θ) - \frac{1}{2} = 0

What is the general solution for sin^2(x)-cos^2(x)+cos(x)=0 ?
The general solution for sin^2(x)-cos^2(x)+cos(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=2pin