Question

cotA+cosecA-1/cotA-cosecA+1=1+cosA/sinA prove that

Answer 1

Next steps are:

cosA/sinA + 1/sinA

cos A +1/sinA .........(proved)

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Answer 2

$\frac{cotA + cosecA - 1}{cotA - cosecA + 1} \\ \\ = \frac{(cotA + cosecA) - ( {cosec}^{2}A - {cot}^{2} A)}{cotA - cosecA + 1} \\ \\ = \frac{(cosecA + cotA)(1 - cosecA + cotA) }{cotA - cosecA + 1}$

$= cosecA + cotA \\ \\ = \frac{1 + cosA}{sinA}$