Question

1)1/ctg(a)+cos(a)/1+sin(a)
2)1/cos(a)-cos(a)
Помогите пожалуйста решить

Answer 1

$1) \ dfrac{1}{ctg alpha } + dfrac{cos alpha }{1+sin alpha } = \ \ = dfrac{sin alpha }{cos alpha } + dfrac{cos alpha }{1+sin alpha }= \ \ = dfrac{(1+sin alpha )sin alpha +cos^2 alpha }{(1+sin alpha )cos alpha } = \ \ = dfrac{sin alpha +sin^2 alpha +cos^2 alpha }{(1+sin alpha )cos alpha } = \ \ = dfrac{1+sin alpha }{(1+sin alpha )cos alpha }= \ \ = dfrac{1}{cos alpha } \ \ 2) \ dfrac{1}{cos alpha } -cos alpha =$
$= dfrac{1-cos^2 alpha }{cos alpha } = \ \ = dfrac{sin^2 alpha }{cos alpha }$