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

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

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

sin^{2} (x) - sin (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^{2} (x) - sin (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

12 cos^{2} (x) + sin (x) - 6 = 0

sin (A) = \frac{3}{5}

tan (θ) = 0.2

sin (x) tan (x) = sin (x), 0 \leq x \leq 2 π

2 tan (x) + sec^{2} (x) = 4

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