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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Rewrite using trig identities

sin (x) + 4 cos^{2} (x) sin (x) = 0

Factor

sin (x) + 4 cos^{2} (x) sin (x) : sin (x) (4 cos^{2} (x) + 1)

sin (x) (4 cos^{2} (x) + 1) = 0

Solving each part separately

sin (x) = 0 or 4 cos^{2} (x) + 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 cos^{2} (x) + 1 = 0 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

4 cos (x) + 1 = 3

y, x = sin (y)

sin (x) + sin (x) cos (x) = 0

tan (x) = \frac{5}{5}

sin (θ) cos (θ) = 0

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