Question

If f(x)=sinx and g(x)=cosx, then the set for all x for which f'(x)=g'(x) is:
A. Pi/4 + k(pi)
B. Pi/2 + k(pi)
C. 3pi/4 +k(pi)
D. Pi/2 + 2k(pi)
E. 3pi/2 + 2k(pi)

Answer 1

f(x) = sinx ---> f ' (x) = cosx
g(x) = cosx ---> g ' (x) = -sinx

so we want -sinx = cosx
-sinx/cosx = 1
tanx = -1
I know tan 3π/4 = -1 and tan 7π/4 = -1
and the period of tanx is π

since 3π/4 + π = 7π/4 we can just state that first answer, and

x = 3π/4 + kπ , where k is an integer