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= pi/3+2pin,x=(5pi)/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{π}{3} + 2 πn, x = \frac{5 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{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

(sec (t) - 2) (cot (t) + 1) = 0

tan (θ) = \frac{50}{60}

x, tan^{2} (x) = \frac{3}{2} sec (x)

2 tan^{2} (θ) cos (θ) - tan^{2} (θ) = 0

1 + 2 cot (θ) - 2 cot^{2} (θ) = - 3 cot^{2} (θ)

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= pi/3+2pin,x=(5pi)/3+2pin