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

The general solution for sin^2(x)+sin(x)=-cos^2(x) is x=(3pi)/2+2pin

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

- cos^{2} (x)

from both sides

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

Rewrite using trig identities

sin (x) + 1 = 0

Move

1

to the right side

sin (x) = - 1

General solutions for

sin (x) = - 1

x = \frac{3 π}{2} + 2 πn

arctan (x) = arccos (\frac{3}{4})

tan^{2} (θ) + 7 tan (θ) + 9 = 0

x, cos (x) \cdot cos (y) = 0

3 sec (θ) = 6

cot (x) = csc (x) + 3

What is the general solution for sin^2(x)+sin(x)=-cos^2(x) ?
The general solution for sin^2(x)+sin(x)=-cos^2(x) is x=(3pi)/2+2pin