Final answer to the problem
true
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...
Can't find a method? Tell us so we can add it.
1
Starting from the left-hand side (LHS) of the identity
$\cot\left(x\right)\sec\left(x\right)$
2
Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
$\frac{\cos\left(x\right)}{\sin\left(x\right)}\sec\left(x\right)$
Why does cot(x) = cos(x)/sin(x) ?
3
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
$\frac{\cos\left(x\right)}{\sin\left(x\right)}\frac{1}{\cos\left(x\right)}$
4
Multiplying fractions $\frac{\cos\left(x\right)}{\sin\left(x\right)} \times \frac{1}{\cos\left(x\right)}$
$\frac{\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}$
5
Simplify the fraction $\frac{\cos\left(x\right)}{\sin\left(x\right)\cos\left(x\right)}$ by $\cos\left(x\right)$
$\frac{1}{\sin\left(x\right)}$
6
The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$
$\csc\left(x\right)$
7
Since we have reached the expression of our goal, we have proven the identity
true
Final answer to the problem
true
