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

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)

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

Solving each part separately

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

tan (x) = 0 : x = πn

sin (x) + 9 = 0 :

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