What is the general solution for 5tan(x)sin(x)=6sin(x) ?

The general solution for 5tan(x)sin(x)=6sin(x) is x=2pin,x=pi+2pin,x=0.87605…+pin

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5tan(x)sin(x)=6sin(x)

5 tan (x) sin (x) = 6 sin (x)

x = 2 πn, x = π + 2 πn, x = 0.87605 \dots + πn

Solution steps

5 tan (x) sin (x) = 6 sin (x)

Subtract

6 sin (x)

from both sides

5 tan (x) sin (x) - 6 sin (x) = 0

Factor

5 tan (x) sin (x) - 6 sin (x) : sin (x) (5 tan (x) - 6)

sin (x) (5 tan (x) - 6) = 0

Solving each part separately

sin (x) = 0 or 5 tan (x) - 6 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

5 tan (x) - 6 = 0 : x = arctan (\frac{6}{5}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (\frac{6}{5}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = 0.87605 \dots + πn

2 tan^{3} (x) - 6 tan (x) = 0

cos (4 x) (2 cos (x) + 1) = 0

cos (3 x) - 1 = 0

sec^{2} (x) + tan^{2} (x) - 3 = 0

tan (α) = \frac{3}{4}

What is the general solution for 5tan(x)sin(x)=6sin(x) ?
The general solution for 5tan(x)sin(x)=6sin(x) is x=2pin,x=pi+2pin,x=0.87605…+pin