What is the general solution for 9sin(x)tan(x)-2tan(x)=0 ?

The general solution for 9sin(x)tan(x)-2tan(x)=0 is x=pin,x=0.22409…+2pin,x=pi-0.22409…+2pin

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9sin(x)tan(x)-2tan(x)=0

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

x = πn, x = 0.22409 \dots + 2 πn, x = π - 0.22409 \dots + 2 πn

Solution steps

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

Factor

9 sin (x) tan (x) - 2 tan (x) : tan (x) (9 sin (x) - 2)

tan (x) (9 sin (x) - 2) = 0

Solving each part separately

tan (x) = 0 or 9 sin (x) - 2 = 0

tan (x) = 0 : x = πn

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

Combine all the solutions

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

Show solutions in decimal form

x = πn, x = 0.22409 \dots + 2 πn, x = π - 0.22409 \dots + 2 πn

3 cot (3 x) + 1 = 0

tan (4 x) = 3

cos (x) + 2 = - cos (x)

- sin^{2} (x) = 0

4 cos (2 x) = 23

What is the general solution for 9sin(x)tan(x)-2tan(x)=0 ?
The general solution for 9sin(x)tan(x)-2tan(x)=0 is x=pin,x=0.22409…+2pin,x=pi-0.22409…+2pin