Expand and simplify the trigonometric expression sin(x)(csc(x)+1)

 Exercise

$sen\left(x\right)\cdot\left(csc\left(x\right)+1\right)$

 

Multiply the single term $\sin\left(x\right)$ by each term of the polynomial $\left(\csc\left(x\right)+1\right)$

$\csc\left(x\right)\sin\left(x\right)+\sin\left(x\right)$

 

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

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

 

Multiplying the fraction by $\sin\left(x\right)$

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

 

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

$1+\sin\left(x\right)$

$1+\sin\left(x\right)$

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