** Final answer to the problem

**

** Step-by-step Solution **

** How should I solve this problem?

- Prove from LHS (left-hand side)
- Prove from RHS (right-hand side)
- Express everything into Sine and Cosine
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Load more...

**

**

Starting from the left-hand side (LHS) of the identity

**

**

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

**Why is tan(x) = sin(x)/cos(x) ?

**

**

Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$

**Why does cot(x) = cos(x)/sin(x) ?

**

**

The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

**

**

Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete

**

**

Combine and simplify all terms in the same fraction with common denominator $\cos\left(x\right)\sin\left(x\right)$

**

**

Applying the trigonometric identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$

**

**

Any expression multiplied by $1$ is equal to itself

**

**

The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$

**

**

Since we have reached the expression of our goal, we have proven the identity

** Final answer to the problem

**