Question

упростить выражение
$1+tg^2x+\frac{1}{sin^2x}$

Answer 1

Ответ:

$= \frac{4}{ {sin}^{2}2x}$

Пошаговое объяснение:

$1 + {tg}^{2} x + \frac{1}{ {sin}^{2}x} = (1 + {tg}^{2} x) + \frac{1}{ {sin}^{2}x} = \frac{1}{ {cos}^{2}x} + \frac{1}{ {sin}^{2}x} = \frac{ {sin}^{2}x + {cos}^{2}x }{ {sin}^{2}x \times {cos}^{2}x } = \frac{1}{ {(sinx \times cosx)}^{2}} = \frac{1}{ {( \frac{1}{2} \times 2 \times sinx \times cosx) }^{2}} = \frac{1}{ \frac{1}{4} \times (2 \times sinx \times cosx)^{2}} = \frac{4}{ {(sin2x)}^{2}} = \frac{4}{ {sin}^{2}2x}$