What is the general solution for 10sin(x)tan(x)-9tan(x)=0 ?

The general solution for 10sin(x)tan(x)-9tan(x)=0 is x=pin,x=1.11976…+2pin,x=pi-1.11976…+2pin

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10sin(x)tan(x)-9tan(x)=0

10 sin (x) tan (x) - 9 tan (x) = 0

x = πn, x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

Solution steps

10 sin (x) tan (x) - 9 tan (x) = 0

Factor

10 sin (x) tan (x) - 9 tan (x) : tan (x) (10 sin (x) - 9)

tan (x) (10 sin (x) - 9) = 0

Solving each part separately

tan (x) = 0 or 10 sin (x) - 9 = 0

tan (x) = 0 : x = πn

10 sin (x) - 9 = 0 : x = arcsin (\frac{9}{10}) + 2 πn, x = π - arcsin (\frac{9}{10}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (\frac{9}{10}) + 2 πn, x = π - arcsin (\frac{9}{10}) + 2 πn

Show solutions in decimal form

x = πn, x = 1.11976 \dots + 2 πn, x = π - 1.11976 \dots + 2 πn

- sin (t) = 0

cos (x) = 4

tan (x) = \frac{5}{6}

2 cos (θ) = - 3

cos (t) = \frac{3}{2}

What is the general solution for 10sin(x)tan(x)-9tan(x)=0 ?
The general solution for 10sin(x)tan(x)-9tan(x)=0 is x=pin,x=1.11976…+2pin,x=pi-1.11976…+2pin