Mathematics: Ineed step by step explanation and answer

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Ineed step by step explanation and answer - id1077976, andybiersack154

Ответ:

simon48

13.03.2022

Mathematics

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

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

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