Question

Simplifica la expresión: sen⁡x/csc⁡x + cos⁡x/sec⁡x 2. Simplifica la expresión: (tan⁡x + cot⁡x)/sec⁡x 3. Simplifica la expresión: cos⁡x(1-csc^2⁡x )

Answer 1

¡Hola!

Simplificar la siguientes expresiones:

$-----------------$
EJERCICIO A.

$A = \frac{ \sin(x) }{ \csc(x) } + \frac{ \cos(x) }{ \sec(x) } \\ A = \sin(x) \times \frac{1}{ \sin(x) } + \cos(x) \times \frac{1}{ \cos(x) } \\ A = 1 + 1 \\ \boxed{ A = 2}$
$-----------------$
EJERCICIO B.

$B = \frac{ \tan(x) + \cot(x) }{ \sin(x) } \\ B = \frac{ \frac{ \sin(x) }{ \cos(x) } + \frac{ \cos(x) }{ \sin(x) } }{ \frac{1}{ \cos(x) } } \\ B = \frac{ \frac{ \sin {}^{2} (x) + \cos {}^{2} (x) }{ \sin(x) \cos(x) } }{ \frac{1}{ \cos(x) } } \\ B = \frac{ \frac{1}{ \sin(x) \cos(x) } }{ \frac{1}{ \cos(x) } } \\ B = \frac{ \cos(x) }{ \sin(x) \cos(x) } \\ B = \frac{1}{ \sin(x ) } \\ \boxed{B = \csc(x) }$
$-----------------$
EJERCICIO C.

$C = \cos(x) (1 - \csc {}^{2} (x) ) \\ C = \cos(x) (1 - \frac{1}{ \sin {}^{2} (x) } ) \\ C = \cos(x) ( \frac{ \sin {}^{2} (x) - 1}{ \sin {}^{2} (x) }) \\ C = \cos(x) ( \frac{ - (1 - \sin {}^{2} (x)) }{ \sin {}^{2} (x) }) \\ C = \cos(x) ( - \frac{ \cos {}^{2} (x) }{ \sin {}^{2} ( x) } ) \\ \boxed{C = - \frac{ \cos {}^{3} (x) }{ \sin {}^{2} (x) } }$
$-----------------$




Espero que te sirva, Saludos.