Question

I need step by step explanation and answer please

Answer 1

Answer:

2

Step-by-step explanation:

Trigonometric identities:

$\sin^{2} (x) + { \cos}^{2} (x) = 1 \\ {\cos}^{2} (x) = 1 - { \sin}^{2} (x) \\ { \sin }^{2} x = 1 - {\cos}^{2} (x) \:$

Replace into the equation

$\frac{ \sqrt{1 - \cos^{2} (x) } }{ \sin(x) } + \frac{ \sqrt{1 - \sin^{2}(x) } }{ \cos(x) } \\ \\ = \frac{ \sqrt{ \sin^{2}(x) } }{ \sin(x) } + \frac{ \sqrt{ \cos^{2}(x) } }{ \cos(x) }$

Remove roots and simply

$= \frac{ \sin(x) }{ \sin(x) } + \frac{ \cos(x) }{ \cos(x) } \\ \\ = 1 + 1 \\ = 2$