Question

Demuestra que sec2 + csc2 = sec2 csc2

Answer 1

Explicación paso a paso:

lhs=

${ \sec(a) }^{2} + { \csc(a) }^{2} = \\ \frac{1}{ { \cos(a) }^{2} } + \frac{1}{ { \sin(a) }^{2} } = \frac{ { \ \ { \sin(a) }^{2} + { cos(a) }^{2} }^{} }{ { { \cos(a) }^{2} \times \ { \sin(a) }^{2} }^{} }$

$= \frac{1}{ { \cos(a) }^{2}. { \sin(a) }^{2} } \\ = \frac{1}{ { \cos(a) }^{2} } \times \frac{1}{ { \sin(a) }^{2} } \\ = { \sec(a) }^{2} \times { \csc(a) }^{2}$