Question

((cotx+cscx)/(sinx+tanx))=cotxcscx

Please prove left side equal to right side, only doing doing work on the left.

Answer 1

LS = (cotx + cscx)/(sinx + tanx)
= (cosx/sinx + 1/sinx)/(sinx + sinx/cosx)
= ( (cox + 1)/sinx) / ( (sinxcosx + sinx)/cosx)
= (cosx + 1)/sinx * cox/(sinx(cosx + 1)
= cotx (cosx + 1)/(sinx(cosx + 1) )
= cotx (1/sinx)
= cotx cscx

= RS