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

The general solution for sin(2x)*cos(3x)=0 is x=pin,x= pi/2+pin,x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3

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sin(2x)*cos(3x)=0

sin (2 x) \cdot cos (3 x) = 0

x = πn, x = \frac{π}{2} + πn, x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Solution steps

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

Solving each part separately

sin (2 x) = 0 or cos (3 x) = 0

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

cos (3 x) = 0 : x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

Combine all the solutions

x = πn, x = \frac{π}{2} + πn, x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

sin^{2} (x) = - 3

cos (θ) = - \frac{2}{7}

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

cos (x) = - \frac{7}{14 5}

k, cos (k l) = 0

What is the general solution for sin(2x)*cos(3x)=0 ?
The general solution for sin(2x)*cos(3x)=0 is x=pin,x= pi/2+pin,x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3