What is the general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 ?

The general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 is x=1.03037…+pin

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5cos(x)cot(x)-3cos(x)-10cot(x)+6=0

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

x = 1.03037 \dots + πn

Solution steps

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

Factor

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 : (5 cot (x) - 3) (cos (x) - 2)

(5 cot (x) - 3) (cos (x) - 2) = 0

Solving each part separately

5 cot (x) - 3 = 0 or cos (x) - 2 = 0

5 cot (x) - 3 = 0 : x = arccot (\frac{3}{5}) + πn

cos (x) - 2 = 0 :

No Solution

Combine all the solutions

x = arccot (\frac{3}{5}) + πn

Show solutions in decimal form

x = 1.03037 \dots + πn

cos (x) = \frac{- 1}{2}

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

y, cos (y) = x

\frac{sin ^{2} ( x )}{1 + cos ( x )} = 1

1 + sin (x) = cos (x)

What is the general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 ?
The general solution for 5cos(x)cot(x)-3cos(x)-10cot(x)+6=0 is x=1.03037…+pin