Question

Докажите тождество, срочно помогите!!! ​

Answer 1

$1.\\(1-tg(x))^2 + (1+tg(x))^2 = 1 + tg^2(x) - 2tg(x) + 1 + tg^2(x) + 2tg(x) = 2(1+tg^2(x)) = 2 * \frac{1}{cos^2(x)} = \frac{2}{cos^2(x)} \\2.\\(ctg^2(x) - cos^2(x))tg^2(x) = ctg^2(x)tg^2(x) - cos^2(x)tg^2(x) = 1 - sin^2(x) = cos^2(x)\\3.\\\frac{cos^3(x)-sin^3(x)}{1-sin(x)cos(x)} = \frac{(cos(x)-sin(x))(cos^2(x)+sin(x)cos(x) + sin^2(x))}{1-sin(x)cos(x)} = \frac{(cos(x)-sin(x))(1+sin(x)cos(x))}{1-sin(x)cos(x)} \neq cos(x)-sin(x)$