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

The general solution for 4sin(x)=sin(x)tan(x) is x=2pin,x=pi+2pin,x=1.32581…+pin

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

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

x = 2 πn, x = π + 2 πn, x = 1.32581 \dots + πn

Solution steps

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

Subtract

sin (x) tan (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

tan (x) - 4 = 0 : x = arctan (4) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (4) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 1.32581 \dots + πn

cos (x) = 0.707

4 cos^{2} (x) - 4 cos (x) - 3 = 0

cot (x) = \frac{4}{3}

tan (θ) = - \frac{5}{2}

- 1 = cos (t) + cos (2 t)

What is the general solution for 4sin(x)=sin(x)tan(x) ?
The general solution for 4sin(x)=sin(x)tan(x) is x=2pin,x=pi+2pin,x=1.32581…+pin