Question

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

Answer 1

Dear student,

LHS
= (cosecA – sinA).(secA – cosA)

= (1/sinA - SinA).(1/cosA - cosA)

= [(1-Sin^2A)/SinA].[[1-cos^2A)/Cosa]

= [cos^2A/SinA].[Sin^2A/CosA] {cancelling equal terms on Nr and Dr We get}

= cosA.SinA

RHS

= 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

Regards