Question

Спростіть вираз 3 и 4 ДАЮ 30 БАЛОВ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

Ответ:

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

....

$tgx + \frac{cosx}{1 + sinx} = \\ = \frac{sinx}{cosx} + \frac{cosx}{1 + sinx} = \\ = \frac{sinx(1 + sinx) + cos ^{2}x }{cosx(1 + sinx)} = \\ = \frac{sinx + {sin}^{2}x + cos^{2}x }{cosx(1 + sinx)} = \\ = \frac{sinx + 1}{cosx(1 + sinx)} = \frac{1}{cosx}$

Пошаговое объяснение:

единственная формула:

${sin}^{2} \alpha + {cos}^{2} \alpha = 1$