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

The general solution for sin(x)tan(x)=3sin(x) is x=2pin,x=pi+2pin,x=1.24904…+pin

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

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

x = 2 πn, x = π + 2 πn, x = 1.24904 \dots + πn

Solution steps

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

Subtract

3 sin (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) - 3 = 0 : x = arctan (3) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (3) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.24904 \dots + πn

12 tan (θ) + 5 = 5 tan (θ) + 5

1 - sin (x) - 2 sin^{2} (x) = 0

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

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

\frac{6}{π} = 3 cos (2 x)

What is the general solution for sin(x)tan(x)=3sin(x) ?
The general solution for sin(x)tan(x)=3sin(x) is x=2pin,x=pi+2pin,x=1.24904…+pin