What is the general solution for -4sin(x)cos(x)=2sin(x) ?

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

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

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

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

Subtract

2 sin (x)

from both sides

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

Factor

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

- 2 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

7 sin^{2} (θ) + 16 sin (θ) + 9 = 0

3 tan (\frac{3 π}{4} (x + \frac{3 π}{2})) = 1

tan (x) = \frac{10}{4}

3 tan^{2} (x) + 11 tan (x) + 8 = 0

4 sin^{2} (x - \frac{π}{3}) = 3

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