Simplify the trigonometric expression (1+cos(w))/sin(w)

 Exercise

$\:\frac{1\:+cos\:w}{sen\:w}$

 

Expand the fraction $\frac{1+\cos\left(w\right)}{\sin\left(w\right)}$ into $2$ simpler fractions with common denominator $\sin\left(w\right)$

$\frac{1}{\sin\left(w\right)}+\frac{\cos\left(w\right)}{\sin\left(w\right)}$

 

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

$\csc\left(w\right)+\frac{\cos\left(w\right)}{\sin\left(w\right)}$

 

Apply the trigonometric identity: $\frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$$=\cot\left(\theta \right)$, where $x=w$

$\csc\left(w\right)+\cot\left(w\right)$

 Why is cos(x)/sin(x) = cot(x) ?

$\csc\left(w\right)+\cot\left(w\right)$

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