2cos3xcosx = cos2C + cosC

By Rania Kashi (P3223) on Saturday, February 24, 2001 - 02:57 pm :

This question has stumped me and its only worth 2 marks!! What am I missing?? I don't know what to do for it, please help!

2cos3xcosx = cos2C + cosC
Express C in terms of x.

By Kerwin Hui (Kwkh2) on Saturday, February 24, 2001 - 04:35 pm :

We have

$2 \cos A \cos B \equiv \cos (A + B) + \cos (A - B)$

so, substituting $A = 3 x$ , $B = x$ gives

$2 \cos 3 x \cos x \equiv \cos 4 x + \cos 2 x$

so, since the displayed equation holds for all $x$ , we have $C = 2 n π \pm 2 x$

Kerwin