how do i ,prove: 1/(sec x-1) + 1/(sec x-1)= 2cotx cscx

Answer 1

LS , using common denominator

= ( secx - 1 + secx + 1)/(sec^2 -1)
= 2secx/tan^2x
= 2/cosx / [(sin^2 x)/cos^2 x]
= 2cosx/sin^2x
= 2cosx/sinx / sinx
= 2cotx cscx
= RS