Question

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$\color{blue}\fbox \color{red}{Prove\:That\:}$
[/tex]\sf{cosec - cot = \frac{sin}{1 + cos} }[/tex]

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Answer 1

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Answer 2

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$\sf\begin{gathered} \frac{ \sin(a) }{1 - \cos(a) } \\ = \frac{ \sin(a) }{1 - \cos(a) } \times \frac{1 + \cos(a) }{1 + \cos(a) } \\ = \frac{ \sin(a)(1 + \cos(a) }{1 - { (\cos(a)) }^{2} } \\ = \frac{ \sin(a)(1 + \cos(a) }{ ({ \sin(a)) }^{2} } \\ = \frac{1 + \cos(a) }{ \sin(a) } \\ = \frac{1}{ \sin(a) } + \frac{ \cos(a) }{ \sin(a) } \\ = \csc(a) + \cot(a) \end{gathered}$

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