What is the general solution for -cot(x)-3cos(x)=-cot(x)cos(x)-3cos(x) ?

The general solution for -cot(x)-3cos(x)=-cot(x)cos(x)-3cos(x) is x= pi/2+pin

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-cot(x)-3cos(x)=-cot(x)cos(x)-3cos(x)

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

x = \frac{π}{2} + πn

Solution steps

- cot (x) - 3 cos (x) = - cot (x) cos (x) - 3 cos (x)

Subtract

- cot (x) cos (x) - 3 cos (x)

from both sides

- cot (x) + cot (x) cos (x) = 0

Factor

- cot (x) + cot (x) cos (x) : cot (x) (cos (x) - 1)

cot (x) (cos (x) - 1) = 0

Solving each part separately

cot (x) = 0 or cos (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

cos (x) - 1 = 0 : x = 2 πn

Combine all the solutions

x = \frac{π}{2} + πn, x = 2 πn

Since the equation is undefined for:

2 πn

x = \frac{π}{2} + πn

6 cos^{2} (x) + 3 cos (x) = 0

6 sin (A) + 4 = 2 sin (A) + 8

(cot (x) - 3) (2 sin (x) + 1) = 0

x, tan (x) = 3

0 = cos (4 x)

What is the general solution for -cot(x)-3cos(x)=-cot(x)cos(x)-3cos(x) ?
The general solution for -cot(x)-3cos(x)=-cot(x)cos(x)-3cos(x) is x= pi/2+pin