Question

prove 1+cosecA 1-sinA=cosA cotA

Answer 1

(1+1/sinA)(1-sinA)=CosA CotA
=(1+SinA)/SinA (1-SinA)
=(1-Sin(square)A/SinA
=Cos(square)A/SinA
=CotA SinA
hence proved...

Answer 2

$=(1-sinA)(1+\frac{1}{sinA})\\\\=(1-sinA)(\frac{sinA+1}{sinA})\\\\=\frac{(1-sinA)(sinA+1)}{sinA} \\\\=\frac{(1)^2-sin^2A}{sinA} \\\\=\frac{cos^2A}{sinA} \\\\=\frac{cosA}{sinA} *cosA\\\\=cotA.cosA$

Proved.