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

The general solution for cos^2(x)+sin^2(x)+sin(x)= 1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

sin (x) + 1 = \frac{1}{2}

Move

1

to the right side

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

General solutions for

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

tan^{2} (b) = 3

a, sin (a + \frac{b}{2}) = cos (\frac{c}{2})

tan (x) - cot (x) = 2 cot^{2} (x)

cot (\frac{- x + 3 n}{4}) = 0

What is the general solution for cos^2(x)+sin^2(x)+sin(x)= 1/2 ?
The general solution for cos^2(x)+sin^2(x)+sin(x)= 1/2 is x=(7pi)/6+2pin,x=(11pi)/6+2pin