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

The general solution for cos^2(x)-sin^2(x)-sin(x)=0 is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

9 cos^{2} (x) + 18 cos (x) + 9 = 0

cot (3 x) = - \frac{3}{3}

sin (6 θ) = 0

3 cot (x) + 1 = - 2

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

What is the general solution for cos^2(x)-sin^2(x)-sin(x)=0 ?
The general solution for cos^2(x)-sin^2(x)-sin(x)=0 is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin