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

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)

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

5 sin (x) + 7 = 0 :

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