Question

Show that :

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

Answer with complete steps & explanation...

Answer 1

Hi ,

LHS = ( cosA-sinA+1)/(cosA+sinA-1)

=[(cosA-sinA+1)(cosA+sinA+1)]/[(cosA+sinA-1)(cosA+sinA-1)]

= [(cosA+1)²- sin² A]/[(cosA+sinA)² -1²]

= [cos²A+2cosA+1 - sin² A]/[cos² A+sin² A+2sinAcosA -1 ]

= [ cos² A + 2cosA+ cos²A] /( 1 + 2sinAcosA-1)

= (2cos²A+ 2cosA)/(2cosAsinA)

= 2cosA( cosA + 1 ) / 2cosAsinA


= ( cosA + 1 ) / sinA

= cosA/sinA + 1/sinA

= cotA + cosecA

= RHS

I hope this helps you.

:)

Answer 2

Hope this'll be helpful.....