Question

Necesito ayuda con estos ejercicios de demostrar las siguientes identidades,es trigonometria, algun héroe?

Answer 1

Respuesta:

$1)\cot(x) + \sec(x) = \frac{1}{ \tan(x) } + \frac{1}{ \cos(x) } \\ \frac{1}{ \tan(x) } + \frac{1}{ \cos(x) } = \frac{1}{ \tan(x) } + \frac{1}{ \cos(x) }$

$2)\tan(x) \times \cot(x) = \frac{1}{ \cot(x) } \times \frac{1}{ \tan(x) } \\ \frac{1}{ \cot(x) } \times \frac{1}{ \tan(x) } = \frac{1}{ \cot(x) } \times \frac{1}{ \tan(x) }$

$3)\frac{ \sin(x) }{ \csc(x) } + \frac{ \cos(x) }{ \sec(x) } = 1 \\ \frac{ \sin(x) }{ \frac{1}{ \sin(x) } } + \frac{ \cos(x) }{ \frac{1}{ \cos(x) } } = 1 \\ { \sin }^{2} (x) + { \cos }^{2} (x) = 1 \\ 1 = 1$

$4)\tan(x) \times \cos(x) \times \csc(x) = 1 \\ \frac{ \sin(x) }{ \cos(x) } \times \cos(x) \times \frac{1}{ \sin(x) } = 1 \ 1 = 1$

$5)\frac{ \sin(x) + \cos(x) }{ \sin(x) } = 1 + \frac{1}{ \tan(x) } \\ \frac{ \sin(x) }{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } = 1 + \frac{1}{ \tan(x) } \\ 1 + \cot(x) = 1 + \frac{1}{ \tan(x) } \\ 1 + \frac{1}{ \tan(x) } = 1 + \frac{1}{ \tan(x) }$

$7) { \tan}^{2} (x) \times \cos(x) \times \csc(x) = \tan(x) \\ \frac{ { \sin}^{2}(x) }{ { \cos }^{2} (x)} \times \cos(x) \times \frac{1}{ \sin(x) } = \tan(x) \\ \frac{ \sin(x) }{ \cos(x) } = \tan(x) \\ \tan(x) = \tan(x)$