Question

прибавление и дробное деление синусов и косинусов. задание 10.

Answer 1

$frac{(sin alpha +cos alpha ) ^{2}-1 }{ctg alpha -sin alpha *cos alpha } = frac{sin^2 alpha +2sin alpha *cos alpha +cos^2 alpha -1}{ frac{cos alpha }{sin alpha }-sin alpha *cos alpha } = frac{2sin alpha *cos alpha }{ frac{cos alpha -sin^2 alpha*cos alpha }{sin alpha } } =$ $frac{2sin alpha *cos alpha *sin alpha }{cos alpha *(1-sin^2 alpha )} = frac{2sin^2 alpha*cos alpha }{cos alpha *cos^2 alpha } =2tg^2 alpha$