Simplify the trigonometric expression (sin(x)cot(x))/(cos(x)+tan(x))

 Exercise

$\frac{\senx\cot x}{\cos x+\tan x}$

 

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

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

 Why does cot(x) = cos(x)/sin(x) ?

 

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

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

 

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

$\frac{\cos\left(x\right)}{\cos\left(x\right)+\tan\left(x\right)}$

$\frac{\cos\left(x\right)}{\cos\left(x\right)+\tan\left(x\right)}$

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