Question

sin 11п/6*cos13п/6*tg5п/4*ctg5п/3

 

sin5a-sina

__________ *tg3a

cos5a-cosa

Answer 1

1) $sinfrac{11pi}{6}*cosfrac{13pi}{6}*tgfrac{5pi}{4}*ctgfrac{5pi}{3}=sin(2pi-frac{pi}{6})*cos(2pi+frac{pi}{6})*tg(pi+frac{pi}{4})*ctg(2pi-frac{pi}{3}) = -sinfrac{pi}{6}*cosfrac{pi}{6}*tgfrac{pi}{4}(-ctgfrac{pi}{3})=frac{1}{2}*frac{sqrt{3}}{2}*1*frac{1}{sqrt{3}}=frac{1}{4}$

2) $frac{sin5a-sina}{cos5a-cosa}tg3a=frac{2sin2a*cos3a}{-2sin3a*sin2a}*tg3a=-ctg3a*tg3a = -1$