Question

2/3(cos4 30-sin4 45)-3(sin2 60-sec2 45)+1/4cot2 30

Answer 1

$\frac{2}{3} ( { \cos(30) }^{4} - { \sin(45) }^{4} ) - 3( { \sin(60) }^{2} - { \sec(45) }^{2} ) + \frac{1}{4} { \cot(30) }^{2} \\ = \frac{2}{3} ( {( \frac{ \sqrt{3} }{2}) }^{4} - {( \frac{1}{ \sqrt{2} }) }^{4} ) - 3( ({ \frac{ \sqrt{3} }{2}) }^{2} - {( \sqrt{2)} }^{2} ) + \frac{1}{4} {( \sqrt{3)} }^{2} \\ = \frac{2}{3} ( \frac{9}{16} - \frac{1}{4} ) - 3( \frac{3}{4} - 2) + \frac{1}{4} \times 3 \\ = \frac{2}{3} \times \frac{5}{16} + 3 \times \frac{5}{4} + \frac{3}{4} \\ = \frac{5}{24} + \frac{15}{4} + \frac{3}{4} \\ = \frac{5 + 90 + 18}{24} \\ = \frac{113}{24}$