Question

sin(a-b)/sin(a+b) и cos(a-b)/cos(a+b) Выразите через а)tga и tgb б)ctga и ctgb

Answer 1

$frac{sin( alpha - beta )}{sin( alpha + beta } = frac{sin alpha *cos beta -cos beta *sin alpha }{sin alpha *cos beta +cos alpha *sin beta } = frac{ frac{sin alpha *cos beta }{cos alpha *cos beta }- frac{cos alpha *sin beta }{cos alpha *cos beta } }{ frac{sin alpha *cos beta }{cos alpha *cos beta } + frac{cos alpha *sin beta }{cos alpha *cos beta } } = frac{tg alpha -tg beta }{tg alpha +tg beta }$

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

3)$frac{sin( alpha - beta )}{sin( alpha + beta )} = frac{sin alpha *cos beta -cos alpha *sin beta }{sin alpha *cos beta +sin beta *cos alpha } = frac{ frac{sin alpha *cos beta }{sin alpha *sin beta }- frac{cos alpha *sin beta }{sin alpha *sin beta } }{ frac{sin alpha *cos beta }{sin alpha *sin beta }+ frac{cos alpha *sin beta }{sin alpha *sin beta } } = frac{ctg beta -ctg alpha }{ctg beta +ctg alpha }$

4)$frac{cos( alpha - beta )}{cos( alpha + beta )} = frac{cos alpha *cos beta +sin alpha sin beta }{cos alpha *cos beta -sin alpha *sin beta } = frac{ frac{cos alpha *cos beta }{sin alpha *sin beta }+ frac{sin alpha *sin beta }{sin alpha *sin beta } }{ frac{cos alpha *cos beta }{sin alpha *sin beta } - frac{sin alpha *sin beta }{sin alpha *sin beta } } = frac{ctg alpha *ctg beta +1}{ctg alpha *ctg beta -1}$

Answer 2

во втором задании после знака равно в числителе и знаменателе знаки поменяйте на противоположные везде