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

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)

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

7 sin (x) + 8 = 0 :

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