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

The general solution for (csc(x))/(cot(x))=csc(x)sec(x) is No Solution for x\in\mathbb{R}

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(csc(x))/(cot(x))=csc(x)sec(x)

\frac{csc ( x )}{cot ( x )} = csc (x) sec (x)

No Solution for x \in R

Solution steps

\frac{csc ( x )}{cot ( x )} = csc (x) sec (x)

Subtract

csc (x) sec (x)

from both sides

\frac{csc ( x )}{cot ( x )} - csc (x) sec (x) = 0

Simplify

\frac{csc ( x )}{cot ( x )} - csc (x) sec (x) : \frac{csc ( x ) - csc ( x ) sec ( x ) cot ( x )}{cot ( x )}

\frac{csc ( x ) - csc ( x ) sec ( x ) cot ( x )}{cot ( x )} = 0

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

csc (x) - csc (x) sec (x) cot (x) = 0

Factor

csc (x) - csc (x) sec (x) cot (x) : csc (x) (1 - sec (x) cot (x))

csc (x) (1 - sec (x) cot (x)) = 0

Solving each part separately

csc (x) = 0 or 1 - sec (x) cot (x) = 0

csc (x) = 0 :

No Solution

1 - sec (x) cot (x) = 0 :

No Solution

Combine all the solutions

No Solution for x \in R

sin (θ) = \frac{1}{3}

cos (θ) = 0.9

tan^{2} (x) = 2 tan (x)

4 - 4 sin (θ) = 4

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

What is the general solution for (csc(x))/(cot(x))=csc(x)sec(x) ?
The general solution for (csc(x))/(cot(x))=csc(x)sec(x) is No Solution for x\in\mathbb{R}