Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Prouver à partir du LHS (côté gauche)
- Prouver à partir du RHS (côté droit)
- Exprimez tout en sinus et en cosinus
- Equation différentielle exacte
- Équation différentielle linéaire
- Équation différentielle séparable
- Equation différentielle homogène
- Produit de binômes avec terme commun
- Méthode FOIL
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Starting from the left-hand side (LHS) of the identity
Apply the trigonometric identity: $\tan\left(\theta \right)$$=\frac{\sin\left(\theta \right)}{\cos\left(\theta \right)}$
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors
Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete
Combine and simplify all terms in the same fraction with common denominator $\cos\left(x\right)\sin\left(x\right)$
Apply the trigonometric identity: $\frac{n}{\cos\left(\theta \right)}$$=n\sec\left(\theta \right)$, where $n=1$
Apply the trigonometric identity: $\frac{n}{\sin\left(\theta \right)}$$=n\csc\left(\theta \right)$, where $n=\sec\left(x\right)$
Since we have reached the expression of our goal, we have proven the identity
