What is the general solution for tan(x)sin(x)-4tan(x)=-3tan(x) ?

The general solution for tan(x)sin(x)-4tan(x)=-3tan(x) is x=pin

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tan(x)sin(x)-4tan(x)=-3tan(x)

tan (x) sin (x) - 4 tan (x) = - 3 tan (x)

x = πn

Solution steps

tan (x) sin (x) - 4 tan (x) = - 3 tan (x)

Subtract

- 3 tan (x)

from both sides

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

Factor

tan (x) sin (x) - tan (x) : tan (x) (sin (x) - 1)

tan (x) (sin (x) - 1) = 0

Solving each part separately

tan (x) = 0 or sin (x) - 1 = 0

tan (x) = 0 : x = πn

sin (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = πn, x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

x = πn

7 tan (x) sin (x) - 2 sin (x) = 0

5 sec (x) + 5 tan (x) = 5

4 cos (θ) - 2 = 0

tan (\frac{x}{3}) = 1

cos (2 θ) + 8 sin^{2} (θ) = 4

What is the general solution for tan(x)sin(x)-4tan(x)=-3tan(x) ?
The general solution for tan(x)sin(x)-4tan(x)=-3tan(x) is x=pin