What is the general solution for (-2sin(x)-1)/((2+sin(x))^2)=0 ?

The general solution for (-2sin(x)-1)/((2+sin(x))^2)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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(-2sin(x)-1)/((2+sin(x))^2)=0

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

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

Solution steps

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

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

cot (x) = - 8

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

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

\frac{sin ( x )}{1 + cos ( x )} = 3 cot (\frac{x}{2})

sin (θ) = \frac{3}{2}, 0 \leq θ \leq 4 π

What is the general solution for (-2sin(x)-1)/((2+sin(x))^2)=0 ?
The general solution for (-2sin(x)-1)/((2+sin(x))^2)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin