Question

решите пожалуйста, срочно

Answer 1

$frac{1}{ctg alpha} + frac{cosalpha}{1+sinalpha} = tg alpha + frac{cosalpha}{1+sinalpha} = frac{sinalpha}{cosalpha} + frac{cosalpha}{1+sinalpha} =frac{sinalpha(1+sinalpha)+cos^2alpha}{cosalpha(1+sinalpha)} = \ = frac{sinalpha+sin^2alpha+cos^2alpha}{cosalpha(1+sinalpha)} = frac{sinalpha+1}{cosalpha(1+sinalpha)} =frac{1}{cosalpha}$

$frac{1}{cosbeta} - cosbeta = frac{1-cos^2beta}{cosbeta} = frac{1-(1-sin^2beta)}{cosbeta} = frac{sin^2beta}{cosbeta} = sinbetacdotfrac{sinbeta}{cosbeta} = sinbetacdot tgbeta$