What is the general solution for 9tan(x)sin(x)-5sin(x)=0 ?

The general solution for 9tan(x)sin(x)-5sin(x)=0 is x=2pin,x=pi+2pin,x=0.50709…+pin

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9tan(x)sin(x)-5sin(x)=0

9 tan (x) sin (x) - 5 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = 0.50709 \dots + πn

Solution steps

9 tan (x) sin (x) - 5 sin (x) = 0

Factor

9 tan (x) sin (x) - 5 sin (x) : sin (x) (9 tan (x) - 5)

sin (x) (9 tan (x) - 5) = 0

Solving each part separately

sin (x) = 0 or 9 tan (x) - 5 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

9 tan (x) - 5 = 0 : x = arctan (\frac{5}{9}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{5}{9}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.50709 \dots + πn

x, y = arctan (x)

7 cos (x) + 7 sin (x) tan (x) = 14

cot (θ) + 5 csc (θ) = 6

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

7 sin (2 x) sin (x) = 7 cos (x)

What is the general solution for 9tan(x)sin(x)-5sin(x)=0 ?
The general solution for 9tan(x)sin(x)-5sin(x)=0 is x=2pin,x=pi+2pin,x=0.50709…+pin