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

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

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

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

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

Solution steps

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

Subtract

sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

1 = - cot (x)

1 = sec (x)

tan (x) = \frac{6.1}{5.1}

4 csc^{2} (θ) - 1 = 0

- 0.5 cos (x) + 0.8660200000000 \dots sin (x) = - 0.5

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