What is the general solution for 8sin(x)tan(x)+tan(x)=0 ?

The general solution for 8sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.12532…+2pin,x=pi+0.12532…+2pin

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8sin(x)tan(x)+tan(x)=0

8 sin (x) tan (x) + tan (x) = 0

x = πn, x = - 0.12532 \dots + 2 πn, x = π + 0.12532 \dots + 2 πn

Solution steps

8 sin (x) tan (x) + tan (x) = 0

Factor

8 sin (x) tan (x) + tan (x) : tan (x) (8 sin (x) + 1)

tan (x) (8 sin (x) + 1) = 0

Solving each part separately

tan (x) = 0 or 8 sin (x) + 1 = 0

tan (x) = 0 : x = πn

8 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (- \frac{1}{8}) + 2 πn, x = π + arcsin (\frac{1}{8}) + 2 πn

Show solutions in decimal form

x = πn, x = - 0.12532 \dots + 2 πn, x = π + 0.12532 \dots + 2 πn

sin (x) - 3 = cos (x) - 3

sin (x) + 4 csc (x) + 5 = 0

sin (x) = \frac{5}{9}

sin (x) = \frac{5}{3}

tan (3 x) = \frac{1}{3}

What is the general solution for 8sin(x)tan(x)+tan(x)=0 ?
The general solution for 8sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.12532…+2pin,x=pi+0.12532…+2pin