Question

(sin^2 5п/3) / (sin^2 5п/4)

Answer 1

$frac{ sin^{2} frac{5 pi }{3} }{ sin^{ frac{5 pi }{4} } } =( frac{sin frac{5 pi }{3} }{sin frac{5 pi }{4} } ) ^{2} =( frac{sin frac{(6 pi }{3}- frac{ pi }{3})  }{sin( frac{4 pi }{4}+ frac{ pi }{4} )} ) ^{2} =( frac{sin(2 pi - frac{ pi }{3})}{sin( pi + frac{ pi }{4} )} ) ^{2} =( frac{-sin frac{ pi }{3} }{-sin frac{ pi }{4} } ) ^{2} =$
$=( frac{ sqrt{3} }{2}: frac{ sqrt{2} }{2} ) ^{2} =( frac{ sqrt{3} }{ sqrt{2} } ) ^{2} = frac{3}{2} =1,5$