Simplify the trigonometric expression cot(x)/cos(x)

 Exercise

$\frac{\cot x}{\cos x}$

 

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

$\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}$

 Why does cot(x) = cos(x)/sin(x) ?

 

Simplify the fraction $\frac{\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\cos\left(x\right)}$ by $\cos\left(x\right)$

$\frac{1}{\sin\left(x\right)}$

 

Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$

$\csc\left(x\right)$

$\csc\left(x\right)$

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