What is the general solution for 9sin(x)tan(x)=-4tan(x) ?

The general solution for 9sin(x)tan(x)=-4tan(x) is x=pin,x=-0.46055…+2pin,x=pi+0.46055…+2pin

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9sin(x)tan(x)=-4tan(x)

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

x = πn, x = - 0.46055 \dots + 2 πn, x = π + 0.46055 \dots + 2 πn

Solution steps

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

Subtract

- 4 tan (x)

from both sides

9 sin (x) tan (x) + 4 tan (x) = 0

Factor

9 sin (x) tan (x) + 4 tan (x) : tan (x) (9 sin (x) + 4)

tan (x) (9 sin (x) + 4) = 0

Solving each part separately

tan (x) = 0 or 9 sin (x) + 4 = 0

tan (x) = 0 : x = πn

9 sin (x) + 4 = 0 : x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (- \frac{4}{9}) + 2 πn, x = π + arcsin (\frac{4}{9}) + 2 πn

Show solutions in decimal form

x = πn, x = - 0.46055 \dots + 2 πn, x = π + 0.46055 \dots + 2 πn

tan^{2} (θ) - 3 tan (θ) = 0

sin^{2} (x) = 2 cos (x) + 2

2 cos^{2} (x) + 3 cos (x) = 0

y, sin (y) = x

sin (2 x) + 3 cos (x) = 0

What is the general solution for 9sin(x)tan(x)=-4tan(x) ?
The general solution for 9sin(x)tan(x)=-4tan(x) is x=pin,x=-0.46055…+2pin,x=pi+0.46055…+2pin