Question

necesito demostrar esta identidad trigonometrica:

Senx . Tanx = Secx - Cosx

Answer 1

Hola!

Explicación paso a paso:

$\sin(x) . \tan(x) = \sec(x) - \cos(x) \\ \sin(x) . \frac{ \sin(x) }{ \cos(x) } = \frac{1}{ \cos(x) } - \cos(x) \\ \frac{ { \sin }^{2} (x)}{ \cos(x) } = \frac{1 - { \cos }^{2} (x)}{ \cos(x) } \\ {\sin }^{2} (x) = 1 - { \cos }^{2} (x) \\ {\sin }^{2} (x) = {\sin }^{2} (x) \\ 1 = 1$

Nota:

$1 - {\cos }^{2} (x) = {\sin }^{2} (x) \\ porque \: proviene \: de \: la \: identidad \\ {\sin }^{2} (x) + {\cos }^{2} (x) = 1 \\ {\sin }^{2} (x) = 1 - {\cos }^{2} (x)$

ESPERO HABERTE AYUDADO!