Question

Demuestra que sec2 + csc2 = sec2 csc2​

Answer 1

Explicación paso a paso:

lhs,

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