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

The general solution for sin(2x)+sin^2(x)+cos^2(x)=0 is x=(3pi)/4+pin

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Rewrite using trig identities

sin (2 x) + 1 = 0

Move

1

to the right side

sin (2 x) = - 1

General solutions for

sin (2 x) = - 1

2 x = \frac{3 π}{2} + 2 πn

Solve

2 x = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

csc (x) = \frac{1}{cos ( x )}

csc (θ) = (1.201)

3 cos (θ) + 2 = 5 sec (θ), 0 \leq θ < 2 π

2 cos (\frac{π}{4} - 3 x) = 2

3 sec^{2} (x) = sec (x)

What is the general solution for sin(2x)+sin^2(x)+cos^2(x)=0 ?
The general solution for sin(2x)+sin^2(x)+cos^2(x)=0 is x=(3pi)/4+pin