Question

(cosecA-sinA)(secA-cosA)=1/tanA+cotA

Answer 1

Answer
RHS
= (cosecA – sinA).(secA – cosA)
= (1/sinA - SinA).(1/cosA - c0sA)
= [(1-Sin^2A)/SinA].[[1-cos^2A)/Cosa]
= [cos^2A/SinA].[Sin^2A/CosA]
= cosA.SinA

LHS
= 1/(tanA + cotA)
= 1/((SinA/CosA + CosA/SinA)
= cosA.SinA / (sin^2A + cos^2A)
= cosA.SinA {since sin^2A + cos^2A = 1}

So
RHS = LHS