# Solve the equation frac{{{3}{a}{{sin}^{2}{left(thetaright)}} cos{{left(thetaright)}}}}{{{3}{a}{{cos}^{2}{left(thetaright)}} sin{{left(thetaright)}}}}= tan{{left(thetaright)}}

Question
Solve the equation $$\frac{{{3}{a}{{\sin}^{2}{\left(\theta\right)}} \cos{{\left(\theta\right)}}}}{{{3}{a}{{\cos}^{2}{\left(\theta\right)}} \sin{{\left(\theta\right)}}}}= \tan{{\left(\theta\right)}}$$

2020-11-13
$$\frac{{{3}{a}{{\sin}^{2}{\left(\theta\right)}} \cos{{\left(\theta\right)}}}}{{{3}{a}{{\cos}^{2}{\left(\theta\right)}} \sin{{\left(\theta\right)}}}}$$
$$=\frac{{{a}{{\sin}^{2}{\left(\theta\right)}} \cos{{\left(\theta\right)}}}}{{{a}{{\cos}^{2}{\left(\theta\right)}} \sin{{\left(\theta\right)}}}}\ \text{[Cancel the common factor 3]}$$
$$=\frac{{{{\sin}^{2}{\left(\theta\right)}} \cos{{\left(\theta\right)}}}}{{{{\cos}^{2}{\left(\theta\right)}} \sin{{\left(\theta\right)}}}}\ \text{[Cancel the common factor a]}$$
$$=\frac{{ \sin{{\left(\theta\right)}} \cos{{\left(\theta\right)}}}}{{{{\cos}^{2}{\left(\theta\right)}}}}\ \text{[Cancel the common factor sin theta]}$$
$$=\frac{ \sin{{\left(\theta\right)}}}{ \cos{{\left(\theta\right)}}}\ \text{[Cancel the common factor cos theta]}$$
$$= \tan{\theta},\text{Use the following identity:}\ \frac{ \sin{{\left({x}\right)}}}{ \cos{{\left({x}\right)}}}= \tan{{\left({x}\right)}}$$

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