What is the general solution for 7sin(x)tan(x)=-8tan(x) ?

The general solution for 7sin(x)tan(x)=-8tan(x) is x=pin

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7sin(x)tan(x)=-8tan(x)

7 sin (x) tan (x) = - 8 tan (x)

x = πn

Degrees

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

Solution steps

7 sin (x) tan (x) = - 8 tan (x)

Subtract

- 8 tan (x)

from both sides

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

Factor

7 sin (x) tan (x) + 8 tan (x) : tan (x) (7 sin (x) + 8)

7 sin (x) tan (x) + 8 tan (x)

Factor out common term

tan (x)

= tan (x) (7 sin (x) + 8)

tan (x) (7 sin (x) + 8) = 0

Solving each part separately

tan (x) = 0 or 7 sin (x) + 8 = 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

7 sin (x) + 8 = 0 :

No Solution

7 sin (x) + 8 = 0

Move

8

to the right side

7 sin (x) + 8 = 0

Subtract

8

from both sides

7 sin (x) + 8 - 8 = 0 - 8

Simplify

7 sin (x) = - 8

7 sin (x) = - 8

Divide both sides by

7

7 sin (x) = - 8

Divide both sides by

7

\frac{7 sin ( x )}{7} = \frac{- 8}{7}

Simplify

sin (x) = - \frac{8}{7}

sin (x) = - \frac{8}{7}

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = πn

sin^{2} (x) + 2 sin (x) - 3 = 0

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

2 sin (x) cos (x) - sin (x) + 2 cos (x) - 1 = 0

sec^{2} (x) = 2 tan (x)

4 sin^{2} (x) - 8 cos (x) + 1 = 0

What is the general solution for 7sin(x)tan(x)=-8tan(x) ?
The general solution for 7sin(x)tan(x)=-8tan(x) is x=pin