What is the general solution for sin^2(3x)+2sin(x)cos(x)+cos^2(3x)=0 ?

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

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sin^2(3x)+2sin(x)cos(x)+cos^2(3x)=0

sin^{2} (3 x) + 2 sin (x) cos (x) + cos^{2} (3 x) = 0

x = \frac{3 π}{4} + πn

Solution steps

sin^{2} (3 x) + 2 sin (x) cos (x) + cos^{2} (3 x) = 0

Rewrite using trig identities

1 + sin (2 x) = 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

20 sin (t) cos (t) = - 4 sin (t)

cos (x) - cos (2 x) = 0, 0^{\circ} \leq x < 36 0^{\circ}

3 = - 3 cos (θ)

2 cos (θ) - 3 = 0, 0 \leq θ \leq 2 π

- 4 sin (x) = cos^{2} (x) + 1, 0 \leq x \leq 2 π

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