Question 1050262
f(x)=sin(x) and g(x)=cos(x)  ===> f'(x)=cos(x) and g'(x)= -sin(x).

We want f'(a) = g'(a), or cos(a) = -sin(a).

<===> cos(a) + sin(a) = 0.

===> {{{sqrt(2)*((1/sqrt(2))* cos(a) + (1/sqrt(2))*sin(a) )= 0}}}

<===> {{{sqrt(2)*sin(a+pi/4) = 0}}}, or {{{sin(a+pi/4) = 0}}}

====> {{{a + pi/4 = k*pi}}}, where k = ..., -2,-1, 0, 1, 2, 3,.... .

====> {{{highlight(a = -pi/4 + k*pi)}}}