What is the general solution for sin(x)tan(x)=-9tan(x) ?

The general solution for sin(x)tan(x)=-9tan(x) is x=pin

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sin(x)tan(x)=-9tan(x)

sin (x) tan (x) = - 9 tan (x)

x = πn

Degrees

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

Solution steps

sin (x) tan (x) = - 9 tan (x)

Subtract

- 9 tan (x)

from both sides

sin (x) tan (x) + 9 tan (x) = 0

Factor

sin (x) tan (x) + 9 tan (x) : tan (x) (sin (x) + 9)

sin (x) tan (x) + 9 tan (x)

Factor out common term

tan (x)

= tan (x) (sin (x) + 9)

tan (x) (sin (x) + 9) = 0

Solving each part separately

tan (x) = 0 or sin (x) + 9 = 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) + 9 = 0 :

No Solution

sin (x) + 9 = 0

Move

9

to the right side

sin (x) + 9 = 0

Subtract

9

from both sides

sin (x) + 9 - 9 = 0 - 9

Simplify

sin (x) = - 9

sin (x) = - 9

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = πn

cos (x) - cos (3 x) = 0

5 cos (x) tan (x) + 3 tan (x) = 0

2 sec (θ) + 2 = 6

4 cos (x) tan (x) = 3 tan (x)

3 sin (x) = 1 + sin (x)

What is the general solution for sin(x)tan(x)=-9tan(x) ?
The general solution for sin(x)tan(x)=-9tan(x) is x=pin