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

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

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sin(2x)cos(x)=0

sin (2 x) cos (x) = 0

x = πn, x = \frac{π}{2} + πn

Solution steps

sin (2 x) cos (x) = 0

Solving each part separately

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

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

Merge Overlapping Intervals

x = πn, x = \frac{π}{2} + πn

8 cos (x) + 8 sin (x) tan (x) = 16

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

2 cos^{2} (x) - cos (x) = 2 - sec (x)

sin^{4} (x) - cos^{4} (x) = \frac{1}{2}

x, y = tan (x)

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