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

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

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

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

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

Solution steps

- sin (x) + sin^{2} (x) - cos^{2} (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{π}{2} + 2 πn

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

- 1 + sin (x) = - 1

\frac{2}{2} = sin (θ)

cos (a) = 1, 8 b = 1, 5 c = 23

sin (θ) cos (θ) = \frac{2 3}{5}

tan (2 5^{\circ}) = cot (2 x + 5)

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