Question

I need step by step explanation and answer please

Answer 1

2

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

`= ( \sin(x) )/( \sin(x) ) + ( \cos(x) )/( \cos(x) ) \\ \\ = 1 + 1 \\ = 2`