Question

find the derivative of (2x+1)(x-1)÷cos x

Answer 1

Explanation:

Use algebra, trigonometry and the continuity of cos at 0.

limx→0sin2x1−cosx=limx→01−cos2x1−cosx

=limx→0(1−cosx)(1+cosx)1−cosx

=limx→0(1+cosx)

=1+cos(0)=1+1=2

The answer is =1−cosx

********""""""""""Explanation"""""''''"********

We use

sin2x+cos2x=1

sin2x=1−cos2x=(1+cosx)(1−cosx)

Therefore,

sin2x1+cosx=1+cosx(1−cosx)1+cosx

=1−cosx