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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

- cos^{2} (x)

from both sides

sin (x) + sin^{2} (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

cos (9 x) - cos (3 x) = sin (6 x)

1 - cos^{2} (θ) + 3 = 2 sin (θ) + 3

sin (4 θ) = sin (2 θ)

y, x sin (y) = x

cos (2 x) cos (x) + sin (2 x) sin (x) = - 1

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