Question

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

Answer 1

see firstly understand one thing wherever you will see cota+coseca-1 remember one thing that 1 is equal to the formula cosec^2-cot^2=1

and at last substitute the value OF cosec theta and and cot theta and take THEIR LCM.

Answer 2

$\frac{tanA}{1 - cotA} + \frac{cotA}{1 - tanA} \\ \\ = \frac{ \frac{sinA}{cosA} }{ \frac{sinA - cosA}{sinA} } + \frac{ \frac{cosA}{sinA} }{ \frac{cosA - sinA}{cosA} } \\ \\ = \frac{ {sin}^{2} A}{cosA(sinA - cosA)} - \frac{ {cos}^{2}A }{sinA(sinA - cosA)} \\ \\ = \frac{ {sin}^{3} A - {cos}^{3}A }{sinAcosA(sinA - cosA)}$

$= \frac{1 + sinAcosA}{sinAcosA} \\ \\ = 1 + secAcosecA$