Question

$frac{cosB}{1-sinB}$ - $frac{cosB}{1+sinB}$
упростите выражение

Answer 1

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