Verify: (cotx - cscx)(cosx +1) =-sinx ?

1 Answer
Aug 1, 2016

Expand and simplify LHS - Apply identity sin^2x+cos^2x = 1

Explanation:

To verify: (cotx - cscx)(cosx +1) =-sinx

LHS=(cosx/sinx - 1/sinx)(cosx+1)

=1/sinx(cosx-1)(cosx+1)

=1/sinx(cos^2x-1)

Since sin^2x+cos^2x = 1 -> (cos^2x-1) = -sin^2x

LHS =-sin^2x/sinx = -sinx = RHS