Question

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

Answer 1

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