f(x) = 2cos(2x) and g(x) = 4cos(x) + k have a common tangent at x=a (0

Question

f(x) = 2cos(2x) and g(x) = 4cos(x) + k have a common tangent at x=a (0<a<=pi/2) (Continues..)

chillout · Answer

I'm having some problems with it. It's pretty straightforward but it is troubling me.
I know that f'(a) = g'(a) and f(a) = g(a). But I seem to find the point where they are equal quite troubling.

f'(x) = -4sin(2x) and g'(x) = -4sin(x). -4sin(2x) = -4sin(x). This is a pure trig problem. Where both curves intercept each other given the interval?

chillout · Answer

I've tried making cos(2x) into cos²(x)-1. Didn't work.

anonymous · Answer

What about applying the double angle formula on the derivative -4sin(2x)?

chillout · Answer

One second, i'll try.

chillout · Answer

Woah... DIdn't imagine that it'd be that easy. Now I can move forward with the rest of the question, thanks! And btw, a=pi/3.

anonymous · Answer

alright, sounds good