What is the general solution for 9cos(x)tan(x)=-8tan(x) ?

The general solution for 9cos(x)tan(x)=-8tan(x) is x=pin,x=2.66571…+2pin,x=-2.66571…+2pin

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9cos(x)tan(x)=-8tan(x)

9 cos (x) tan (x) = - 8 tan (x)

x = πn, x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn

Solution steps

9 cos (x) tan (x) = - 8 tan (x)

Subtract

- 8 tan (x)

from both sides

9 cos (x) tan (x) + 8 tan (x) = 0

Factor

9 cos (x) tan (x) + 8 tan (x) : tan (x) (9 cos (x) + 8)

tan (x) (9 cos (x) + 8) = 0

Solving each part separately

tan (x) = 0 or 9 cos (x) + 8 = 0

tan (x) = 0 : x = πn

9 cos (x) + 8 = 0 : x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

Combine all the solutions

x = πn, x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

Show solutions in decimal form

x = πn, x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn

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

sin (x) cos (x) = - 9 cos (x)

5 tan (θ) - 7 = 0

cot^{2} (x) + 1 = sin^{2} (x)

(4 + tan (x)) (3 sin (x) - 2) = 0

What is the general solution for 9cos(x)tan(x)=-8tan(x) ?
The general solution for 9cos(x)tan(x)=-8tan(x) is x=pin,x=2.66571…+2pin,x=-2.66571…+2pin