What is the general solution for cos(x)=(cos(x))/(csc(x)) ?

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

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cos(x)=(cos(x))/(csc(x))

cos (x) = \frac{cos ( x )}{csc ( x )}

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

Solution steps

cos (x) = \frac{cos ( x )}{csc ( x )}

Subtract

\frac{cos ( x )}{csc ( x )}

from both sides

cos (x) - \frac{cos ( x )}{csc ( x )} = 0

Simplify

cos (x) - \frac{cos ( x )}{csc ( x )} : \frac{cos ( x ) csc ( x ) - cos ( x )}{csc ( x )}

\frac{cos ( x ) csc ( x ) - cos ( x )}{csc ( x )} = 0

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

cos (x) csc (x) - cos (x) = 0

Factor

cos (x) csc (x) - cos (x) : cos (x) (csc (x) - 1)

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

Solving each part separately

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

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

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

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

cos (θ) = \frac{1}{1 ^{2} + ( 4 ) ^{2} + 8 ^{2}}

2 + 3 cot^{2} (x) - 3 csc (x) = 5

- 2 = - 2 + tan (θ)

cos (A) = 0.65

sin (3 x - \frac{π}{4}) = \frac{2}{2}

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