Final Answer
true
Step-by-step solution
Problem to solve:
$\cot\left(x\right)\cdot\sec\left(x\right)=\csc\left(x\right)$
Solving method
1
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
$\frac{\cot\left(x\right)}{\cos\left(x\right)}=\csc\left(x\right)$
2
Apply the trigonometric identity: $\cot(x)=\frac{\cos(x)}{\sin(x)}$
$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}=\csc\left(x\right)$
3
Simplify the fraction $\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}$ by $\cos\left(x\right)$
$\frac{1}{\sin\left(x\right)}=\csc\left(x\right)$
4
The reciprocal sine function is cosecant: $\frac{1}{\sin(x)}=\csc(x)$
$\csc\left(x\right)=\csc\left(x\right)$
5
Since both sides of the equality are equal, we have proven the identity
true
Final Answer
true