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

The general solution for -3cos^2(u)sin(u)-2sin(2u)=0 is u=2pin,u=pi+2pin,u= pi/2+2pin,u=(3pi)/2+2pin

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-3cos^2(u)sin(u)-2sin(2u)=0

- 3 cos^{2} (u) sin (u) - 2 sin (2 u) = 0

u = 2 πn, u = π + 2 πn, u = \frac{π}{2} + 2 πn, u = \frac{3 π}{2} + 2 πn

Solution steps

- 3 cos^{2} (u) sin (u) - 2 sin (2 u) = 0

Rewrite using trig identities

- 3 cos^{2} (u) sin (u) - 4 cos (u) sin (u) = 0

Factor

- 3 cos^{2} (u) sin (u) - 4 cos (u) sin (u) : - sin (u) cos (u) (3 cos (u) + 4)

- sin (u) cos (u) (3 cos (u) + 4) = 0

Solving each part separately

sin (u) = 0 or cos (u) = 0 or 3 cos (u) + 4 = 0

sin (u) = 0 : u = 2 πn, u = π + 2 πn

cos (u) = 0 : u = \frac{π}{2} + 2 πn, u = \frac{3 π}{2} + 2 πn

3 cos (u) + 4 = 0 :

No Solution

Combine all the solutions

u = 2 πn, u = π + 2 πn, u = \frac{π}{2} + 2 πn, u = \frac{3 π}{2} + 2 πn

cot (θ) = - \frac{7}{24}

2 sin (x) + 2 cos (x) = 6

0 = - 0.65 sin (13 x)

x, tan^{2} (x) - 1 = 0

c^{9} = 3 tan (- 3 x + c)

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