What is the general solution for 5sin(x)tan(x)=-7tan(x) ?

The general solution for 5sin(x)tan(x)=-7tan(x) is x=pin

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5sin(x)tan(x)=-7tan(x)

5 sin (x) tan (x) = - 7 tan (x)

x = πn

Degrees

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

Solution steps

5 sin (x) tan (x) = - 7 tan (x)

Subtract

- 7 tan (x)

from both sides

5 sin (x) tan (x) + 7 tan (x) = 0

Factor

5 sin (x) tan (x) + 7 tan (x) : tan (x) (5 sin (x) + 7)

5 sin (x) tan (x) + 7 tan (x)

Factor out common term

tan (x)

= tan (x) (5 sin (x) + 7)

tan (x) (5 sin (x) + 7) = 0

Solving each part separately

tan (x) = 0 or 5 sin (x) + 7 = 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

5 sin (x) + 7 = 0 :

No Solution

5 sin (x) + 7 = 0

Move

7

to the right side

5 sin (x) + 7 = 0

Subtract

7

from both sides

5 sin (x) + 7 - 7 = 0 - 7

Simplify

5 sin (x) = - 7

5 sin (x) = - 7

Divide both sides by

5

5 sin (x) = - 7

Divide both sides by

5

\frac{5 sin ( x )}{5} = \frac{- 7}{5}

Simplify

sin (x) = - \frac{7}{5}

sin (x) = - \frac{7}{5}

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = πn

cos (x + \frac{π}{2}) - cos (x - \frac{π}{2}) = 2

tan (2 x) + 1 = sec (2 x)

sin (x) \cdot cos (x) = 0

sin (x) - 5 = cos (x) - 5

cot^{2} (x) csc^{2} (x) - cot^{2} (x) = 9

What is the general solution for 5sin(x)tan(x)=-7tan(x) ?
The general solution for 5sin(x)tan(x)=-7tan(x) is x=pin