Which of the following is the best linear approximation for f(x) = cos(x) near x= π/2

The local linear approximation of f near x = a is given by
                              f(x) ≈ f(a) + f'(a)(x-a)
Evaluating f at π/2
                          f(π/2) = cos(π/2) = 0                        
Since f(x) = cos(x), differentiating gets us
                           f'(x) = -sin(x)
                       f'(π/2) = -sin(π/2) = -1
So the local liner approximation is
                              f(x) ≈ 0+ -1(x-π/2)
                              f(x) ≈ -x+π/2
The answer to this question is -x+π/2

Ais the answer for your question