What is the general solution for 5cot(x)=cos(x) ?

The general solution for 5cot(x)=cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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5cot(x)=cos(x)

5 cot (x) = cos (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

5 cot (x) = cos (x)

Subtract

cos (x)

from both sides

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

Express with sin, cos

\frac{5 cos ( x ) - cos ( x ) sin ( x )}{sin ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

5 cos (x) - cos (x) sin (x) = 0

Factor

5 cos (x) - cos (x) sin (x) : - cos (x) (sin (x) - 5)

- cos (x) (sin (x) - 5) = 0

Solving each part separately

cos (x) = 0 or sin (x) - 5 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (x) - 5 = 0 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin^{2} (x) - 1 = cos (x)

9 sin^{2} (θ) + 19 sin (θ) + 8 = 7 sin (θ) + 4

arccos (x) = \frac{7 π}{8}

\frac{sin ( 3 7 ^{\circ} )}{23} = \frac{sin ( x )}{21}

csc (x) = \frac{1}{3}

What is the general solution for 5cot(x)=cos(x) ?
The general solution for 5cot(x)=cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin