What is the general solution for sin(x)tan(x)-4tan(x)=0 ?

The general solution for sin(x)tan(x)-4tan(x)=0 is x=pin

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

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

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Factor

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

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

Factor out common term

tan (x)

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

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

Solving each part separately

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

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

sin (x) - 4 = 0 :

No Solution

sin (x) - 4 = 0

Move

4

to the right side

sin (x) - 4 = 0

Add

4

to both sides

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

Simplify

sin (x) = 4

sin (x) = 4

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = πn

sec (\frac{θ}{5}) = 7

csc^{2} (x) + 2 cot (x) = 0

2 sin (x) tan (x) - tan (x) = 1 - 2 sin (x)

tan (θ) = \frac{2 3}{3} sin (θ)

tan (4 x) = - 1

What is the general solution for sin(x)tan(x)-4tan(x)=0 ?
The general solution for sin(x)tan(x)-4tan(x)=0 is x=pin