Question

(cotA-1+cosecA)÷(cotA+1-cosecA

Answer 1

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$= \frac{ \cot(a) - 1 + \csc(a) }{ \cot(a) + 1 - \csc(a) } \\ = \frac{ \frac{ \cos(a) }{ \sin(a) } - \frac{1}{ \sin(a) } + \frac{1}{ \sin(a) } }{ \frac{ \cos(a) }{ \sin(a) } + \frac{1}{ \sin(a) } - \frac{1}{ \csc(a) } } \\ = \frac{ \frac{ \ \cos(a) - 1 + 1}{ \sin(a) } }{ \frac{ \cos(a) + 1 - 1 }{ \sin(a) } } \\ = \frac{ \cos(a) }{ \sin(a) } \times \frac{ \sin(a) }{ \cos(a) } \\ = 1$

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