Question

sec² x cot² x - cos² x csc² x = 1​

Answer 1

Hola.

Debemos considerar las siguientes identidades.

$sec^{2}(x) = \frac{1}{cos^{2}(x)}$

$cot^{2}(x) = \frac{cos^{2}(x)}{sen^{2}(x)}$

$csc^{2}(x) = \frac{1}{sen^{2}(x)}$

$sen^{2}(x) = 1 - cos^{2}(x)$

Resolvemos

$sec^{2}(x)*cot^{2}(x) - cos^{2}(x) * csc^{2}(x) = 1$

$\frac{1}{cos^{2}(x)}*\frac{cos^{2}(x)}{sen^{2}(x)} - cos^{2}(x)*\frac{1}{sen^{2}(x)}=1$

$\frac{1}{sen^{2}(x)} - \frac{cos^{2}(x)}{sen^{2}(x)} = 1$

$\frac{1-cos^{2}(x)}{sen^{2}(x)} = 1$

$\frac{sen^{2})x)}{sen^{2}(x)} = 1$

   $1 = 1$     ====> Respuesta

Un cordial saludo.