What is the general solution for 5sin(x)tan(x)+4tan(x)=0 ?

The general solution for 5sin(x)tan(x)+4tan(x)=0 is x=pin,x=-0.92729…+2pin,x=pi+0.92729…+2pin

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

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

x = πn, x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

Solution steps

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

Factor

5 sin (x) tan (x) + 4 tan (x) : tan (x) (5 sin (x) + 4)

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

Solving each part separately

tan (x) = 0 or 5 sin (x) + 4 = 0

tan (x) = 0 : x = πn

5 sin (x) + 4 = 0 : x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

Combine all the solutions

x = πn, x = arcsin (- \frac{4}{5}) + 2 πn, x = π + arcsin (\frac{4}{5}) + 2 πn

Show solutions in decimal form

x = πn, x = - 0.92729 \dots + 2 πn, x = π + 0.92729 \dots + 2 πn

y, tan (y) = x

2 cos (x) + 5 = 4

cos (x) = - 0.64

y, x = tan (\frac{π}{4} y)

2 sin^{2} (x) - 5 sin (x) + 2 = 0, 0 \leq x \leq 2 π

What is the general solution for 5sin(x)tan(x)+4tan(x)=0 ?
The general solution for 5sin(x)tan(x)+4tan(x)=0 is x=pin,x=-0.92729…+2pin,x=pi+0.92729…+2pin