How do you differentiate #f(x)=(tanx-1)/secx# at #x=pi/3#?
1 Answer
Dec 17, 2016
Explanation:
Rewrite in sine and cosine.
#f(x) = (sinx/cosx- 1)/(1/cosx)#
#f(x) = ((sinx - cosx)/cosx)/(1/cosx)#
#f(x) = sinx - cosx#
We differentiate this using
#f'(x) = cosx - (-sinx)#
#f'(x) = cosx + sinx#
We now evaluate
#f'(pi/3) = cos(pi/3) + sin(pi/3)#
#f'(pi/3) = 1/2 + sqrt(3)/2#
#f'(pi/3) = (1 + sqrt(3))/2#
Hopefully this helps!