2 (cos60°)² + (sec30°)² - (tan45°)² / (sin 30°)² + (cos30°)²

[tex] \sec(30) = \frac{1}{ \cos(30) } [/tex]
[tex] \frac{2 ({ \cos(60)) }^{2} + (\sec(30))^{2} - { (\tan(45)) }^{2} }{ ({ \sin(30) )}^{2} + {( \cos(30) )}^{2} } \\ = \frac{2( \frac{1}{2})^{2} + { ( \frac{1}{ \frac{1}{2} \sqrt{3} } ) }^{2} - {1}^{2} }{ { (\frac{1}{2} )}^{2} + { (\frac{1}{2} \sqrt{3} ) }^{2} } \\ = \frac{2 (\frac{1}{4}) + { (\frac{2}{ \sqrt{3} } )}^{2} - 1 }{ \frac{1}{4} + \frac{1}{4} (3)} \\ = \frac{ \frac{2}{4} + \frac{4}{ \sqrt{9} } - 1 }{ \frac{1}{4} + \frac{3}{4} } \\ = \frac{ \frac{2}{4} + \frac{4}{3} - 1}{ \frac{4}{4} } \\ = \frac{ \frac{6}{12} + \frac{16}{12} - \frac{12}{12} }{1} \\ = \frac{6 + 16 - 12}{12} \\ = \frac{10}{12}[/tex]
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