(cotx-cscx)(cosx+1)=-sinx

cotx-cscxcosx1-sinx

#1

(cotx-cscx)(cosx+1)=-sinx

Answer:

(cotx-cscx)(cosx+1)
=(cosx/sinx-1/sinx)(cosx+1) [since cotx=cosx/sinx and cscx=1/sinx)
=(cosx-1)(cosx+1)/sinx
=(cos^2x-1)/sinx [ since (a+b)(a-b)=a^2-b^2 ]
=-sin^2x/sinx [since sin^2x+cos^2x=1 ;cos^2x-1=-sin^2x ]
=-sinx