Question

4 sin альфа минус cos альфа разделить на cos альфа минус 4 sin альфа

Answer 1

$frac{4sin alpha -cos alpha }{cos alpha -4sin alpha } = frac{(4sin alpha -cos alpha )(cos alpha +4sin alpha )}{(cos alpha -4sin alpha)(cos alpha +4sin alpha ) } =$

$=frac{4sin alpha cos alpha +16sin ^{2} alpha -cos ^{2} alpha -4sin alpha cos alpha }{cos ^{2} alpha -16sin ^{2} alpha } =$

$= frac{16sin ^{2} alpha -cos ^{2} alpha }{cos ^{2} -16sin ^{2} alpha }= frac{-cos ^{2} alpha +16sin ^{2} alpha }{cos ^{2} -16sin ^{2} alpha } = frac{-(cos ^{2} -16sin ^{2} alpha) }{cos ^{2} -16sin ^{2} alpha } =-1$