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

The general solution for 10sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.10016…+2pin,x=pi+0.10016…+2pin

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10sin(x)tan(x)+tan(x)=0

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

x = πn, x = - 0.10016 \dots + 2 πn, x = π + 0.10016 \dots + 2 πn

Solution steps

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

Factor

10 sin (x) tan (x) + tan (x) : tan (x) (10 sin (x) + 1)

tan (x) (10 sin (x) + 1) = 0

Solving each part separately

tan (x) = 0 or 10 sin (x) + 1 = 0

tan (x) = 0 : x = πn

10 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

Show solutions in decimal form

x = πn, x = - 0.10016 \dots + 2 πn, x = π + 0.10016 \dots + 2 πn

2 sin^{2} (θ) + sin (θ) - 1 = 0, 0 \leq θ \leq 2 π

10 sin (x) cos (x) - 7 cos (x) = 0

sin (x + \frac{π}{4}) - sin (x - \frac{π}{4}) = 1

2 cos^{3} (x) = 2 cos (x)

sin^{2} (x) + cos^{2} (x) = 2

What is the general solution for 10sin(x)tan(x)+tan(x)=0 ?
The general solution for 10sin(x)tan(x)+tan(x)=0 is x=pin,x=-0.10016…+2pin,x=pi+0.10016…+2pin