Question

$frac{sin87cos63+cos87sin63}{cos24cos21-sin24sin21}$

Answer 1

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

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