$\frac{2 c o s 60 s i n 60 + c o t 45}{3 c o s^{2} 60 - s i n^{2} 45 + 2 t a n^{2} 30}$

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Solution

$\frac{2 c o s 60 s i n 60 + c o t 45}{3 c o s^{2} 60 - s i n^{2} 45 + 2 t a n^{2} 30}$

$= \frac{2 \times \frac{1}{2} \times \frac{\sqrt{3}}{2} + 1}{3 \times \frac{1}{4} - \frac{1}{2} + 2 \times \frac{1}{3}}$

$= \frac{\frac{\sqrt{3}}{2} + 1}{\frac{3}{4} - \frac{1}{2} + \frac{2}{3}}$

$= \frac{\sqrt{3} + 2}{9 - 6 + 8}$

$= \frac{6 (\sqrt{3} + 2)}{11}$

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