What is the general solution for 2sin(x)tan(x)+5tan(x)=0 ?

The general solution for 2sin(x)tan(x)+5tan(x)=0 is x=pin

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2sin(x)tan(x)+5tan(x)=0

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

x = πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n

Solution steps

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

Factor

2 sin (x) tan (x) + 5 tan (x) : tan (x) (2 sin (x) + 5)

2 sin (x) tan (x) + 5 tan (x)

Factor out common term

tan (x)

= tan (x) (2 sin (x) + 5)

tan (x) (2 sin (x) + 5) = 0

Solving each part separately

tan (x) = 0 or 2 sin (x) + 5 = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

2 sin (x) + 5 = 0 :

No Solution

2 sin (x) + 5 = 0

Move

5

to the right side

2 sin (x) + 5 = 0

Subtract

5

from both sides

2 sin (x) + 5 - 5 = 0 - 5

Simplify

2 sin (x) = - 5

2 sin (x) = - 5

Divide both sides by

2

2 sin (x) = - 5

Divide both sides by

2

\frac{2 sin ( x )}{2} = \frac{- 5}{2}

Simplify

sin (x) = - \frac{5}{2}

sin (x) = - \frac{5}{2}

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = πn

tan (3 x) = 3, 0 \leq x \leq 2 π

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

6 sin^{2} (x) + sin (x) - 1 = 0

sin (2 x) - 2 cos^{2} (x) = 0

sin^{2} (x) - 7 cos (x) + 7 = 0

What is the general solution for 2sin(x)tan(x)+5tan(x)=0 ?
The general solution for 2sin(x)tan(x)+5tan(x)=0 is x=pin