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

The general solution for -2sin(2x)sin(x)=sin(2x) is x=pin,x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

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-2sin(2x)sin(x)=sin(2x)

- 2 sin (2 x) sin (x) = sin (2 x)

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

- 2 sin (2 x) sin (x) = sin (2 x)

Subtract

sin (2 x)

from both sides

- 2 sin (2 x) sin (x) - sin (2 x) = 0

Factor

- 2 sin (2 x) sin (x) - sin (2 x) : - sin (2 x) (2 sin (x) + 1)

- sin (2 x) (2 sin (x) + 1) = 0

Solving each part separately

sin (2 x) = 0 or 2 sin (x) + 1 = 0

sin (2 x) = 0 : x = πn, x = \frac{π}{2} + πn

2 sin (x) + 1 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{2} + πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

sin (θ) - 0.2 cos (θ) = \frac{6.25}{9.8}

3 cos (θ) = 8 tan (θ)

tan (\frac{θ}{4}) + 3 = 0

tan (3 r + 2) = 4 5^{\circ}

What is the general solution for -2sin(2x)sin(x)=sin(2x) ?
The general solution for -2sin(2x)sin(x)=sin(2x) is x=pin,x= pi/2+pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin