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

The general solution for 2sin(x)cos(x)=-sin(x) is x=2pin,x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin

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

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

x = 2 πn, x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

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

Subtract

- sin (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

2 cos (x) + 1 = 0 : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

4 cos (x) = 23

tan (x) = \frac{50}{50}

4 tan (θ) = 4

4 cos^{2} (x) - 8 cos (x) + 4 = 0

5 sin (x) cot (x) = 1

What is the general solution for 2sin(x)cos(x)=-sin(x) ?
The general solution for 2sin(x)cos(x)=-sin(x) is x=2pin,x=pi+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin