Answer 1

$\frac{sin87 ^{o}cos63 ^{o}+cos87 ^{o} sin63 ^{o} }{cos24 ^{o}cos21 ^{o} -sin24 ^{o}sin21 ^{o} } = \frac{sin(87 ^{o}+63 ^{o} ) }{cos(24 ^{o} +21 ^{o} )} = \frac{sin150 ^{o} }{cos45 ^{o} } =$

$= \frac{sin(180 ^{o}-30 ^{o}) }{cos45 ^{o} } = \frac{sin30 ^{o} }{cos45 ^{o}} = \frac{ \frac{1}{2} }{ \frac{ \sqrt{2} }{2} } = \frac{1}{ \sqrt{2} } .$