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

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

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

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

x = πn, x = \frac{π}{2} + πn

Solution steps

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

Solving each part separately

sin (2 x) = 0 or sin (x) = 0 or cos (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

Merge Overlapping Intervals

x = πn, x = \frac{π}{2} + πn

sin (4 x) - cos (4 x) = sin (2 x) - cos (2 x)

2 \cdot sin^{2} (x) - 1 = 0

sin^{2} (\frac{x}{2}) = sin^{2} (x)

tan (θ) = \frac{220}{370}

2 tan (2 x) = - 42

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