Helluuu,
I don't really know what to say to introduce myself other than saying that i am a 19 year old, living in brazil who needs very much help!! Sorry, my english is not so good but i try for you to understand.
The book says that i need to proof that this formula is true with all values for x:
(5 cos x-sin x)^{2 }= A cos 2x + B sin 2x+ C
The book also says that A,B,C is a whole number and not decimal or fráction.
I tried to do this:
(5 cos x-sin x)2 = A cos 2x + B sin 2x+ C
25 cos^{2} x-sin^{2}+sin2x=
25 cos^{2} x+sin2x+sin^{2}x=
-1+25 cos^{2} x+sin2x=
24 cos^{2}x-12+12=
12 cos 2x+ sin 2x+ 24
A=12
B=1
C=24
I don't see what is wrong, pleaase help i honestly dont know why?