What is the general solution for 4tan(x)sin(x)=3sin(x) ?

The general solution for 4tan(x)sin(x)=3sin(x) is x=2pin,x=pi+2pin,x=0.64350…+pin

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4tan(x)sin(x)=3sin(x)

4 tan (x) sin (x) = 3 sin (x)

x = 2 πn, x = π + 2 πn, x = 0.64350 \dots + πn

Solution steps

4 tan (x) sin (x) = 3 sin (x)

Subtract

3 sin (x)

from both sides

4 tan (x) sin (x) - 3 sin (x) = 0

Factor

4 tan (x) sin (x) - 3 sin (x) : sin (x) (4 tan (x) - 3)

sin (x) (4 tan (x) - 3) = 0

Solving each part separately

sin (x) = 0 or 4 tan (x) - 3 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

4 tan (x) - 3 = 0 : x = arctan (\frac{3}{4}) + πn

Combine all the solutions

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

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.64350 \dots + πn

3 sin (θ) + cos (θ) = 3

25 cos^{2} (θ) - 9 = 0

sin (θ) = 3 cos (θ)

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

- sin (θ) + cos (2 θ) = 1

What is the general solution for 4tan(x)sin(x)=3sin(x) ?
The general solution for 4tan(x)sin(x)=3sin(x) is x=2pin,x=pi+2pin,x=0.64350…+pin