What is the general solution for 1/(cot(x))-(sec(x))/(csc(x))=cos(x) ?

The general solution for 1/(cot(x))-(sec(x))/(csc(x))=cos(x) is No Solution for x\in\mathbb{R}

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1/(cot(x))-(sec(x))/(csc(x))=cos(x)

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} = cos (x)

No Solution for x \in R

Solution steps

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} = cos (x)

Subtract

cos (x)

from both sides

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} - cos (x) = 0

Simplify

\frac{1}{cot ( x )} - \frac{sec ( x )}{csc ( x )} - cos (x) : \frac{csc ( x ) - sec ( x ) cot ( x ) - cos ( x ) cot ( x ) csc ( x )}{cot ( x ) csc ( x )}

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

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

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

Express with sin, cos

- \frac{cos ^{2} ( x )}{sin ^{2} ( x )} = 0

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

- cos^{2} (x) = 0

Divide both sides by

- 1

cos (x) = 0

General solutions for

cos (x) = 0

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

Since the equation is undefined for:

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

No Solution for x \in R

10 sin (x) + 10 cos^{2} (x) = 10, 0 \leq x < 2 π

sin (x) = 1, 2 π \leq x \leq 4 π

cos (a) = 1

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

sec (θ) = \frac{7}{5}

What is the general solution for 1/(cot(x))-(sec(x))/(csc(x))=cos(x) ?
The general solution for 1/(cot(x))-(sec(x))/(csc(x))=cos(x) is No Solution for x\in\mathbb{R}