Simplify the expression 3tan(60cot(30)sin(45)csc(45))

 Exercise

$3\tan\left(60^{\circ}\cot30^{\circ}\sin45^{\circ}\csc45^{\circ}\right)$

 

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

$3\tan\left(\cot\left(30\right)\sin\left(45\right)\cdot \frac{60}{\sin\left(45\right)}\right)$

 

Multiplying the fraction by $\cot\left(30\right)\sin\left(45\right)$

$3\tan\left(\frac{60\cot\left(30\right)\sin\left(45\right)}{\sin\left(45\right)}\right)$

 

Simplify the fraction $\frac{60\cot\left(30\right)\sin\left(45\right)}{\sin\left(45\right)}$ by $\sin\left(45\right)$

$3\tan\left(60\cot\left(30\right)\right)$

$3\tan\left(60\cot\left(30\right)\right)$

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