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

The general solution for 5tan(x)sin(x)=-7sin(x) is x=2pin,x=pi+2pin,x=-0.95054…+pin

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

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

x = 2 πn, x = π + 2 πn, x = - 0.95054 \dots + πn

Solution steps

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

Subtract

- 7 sin (x)

from both sides

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

5 tan (x) + 7 = 0 : x = arctan (- \frac{7}{5}) + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = arctan (- \frac{7}{5}) + πn

Show solutions in decimal form

x = 2 πn, x = π + 2 πn, x = - 0.95054 \dots + πn

tan (x + π) - cos (x + \frac{π}{2}) = 0

2 cos^{2} (θ) - 9 cos (θ) + 4 = 0

cos (2 x + \frac{π}{4}) = \frac{2}{2}

x, tan (x) = 1

cot (t) = - 3

What is the general solution for 5tan(x)sin(x)=-7sin(x) ?
The general solution for 5tan(x)sin(x)=-7sin(x) is x=2pin,x=pi+2pin,x=-0.95054…+pin