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

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

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(tan(x)+cot(x))/(csc(x))=cos(x)

\frac{tan ( x ) + cot ( x )}{csc ( x )} = cos (x)

No Solution for x \in R

Solution steps

\frac{tan ( x ) + cot ( x )}{csc ( x )} = cos (x)

Subtract

cos (x)

from both sides

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

Simplify

\frac{tan ( x ) + cot ( x )}{csc ( x )} - cos (x) : \frac{tan ( x ) + cot ( x ) - cos ( x ) csc ( x )}{csc ( x )}

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

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

tan (x) + cot (x) - cos (x) csc (x) = 0

Rewrite using trig identities

tan (x) = 0

General solutions for

tan (x) = 0

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = πn

Since the equation is undefined for:

πn

No Solution for x \in R

tan (θ) = - \frac{3}{7}

sin (2 x) = 0, - π \leq x \leq π

cos (2 x) - sin (2 x) = 1

2 cos (θ) = 3 cos (3 θ)

2 sin (\frac{x}{2}) = 2

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