1. ## Hellooo/ Math problem

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.

2. ## Re: Hellooo/ Math problem

Originally Posted by MathChick
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.
$\sin^2(x)=\dfrac{1-\cos(2x)}{2}$

$\cos^2(x)=\dfrac{1+\cos(2x)}{2}$

$\sin(2x)=2\sin(x)\cos(x)$

you should be able to complete this given those 3 identities

3. ## Re: Hellooo/ Math problem

I tried to do this:

(5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

25 cos2 x-sin2+sin2x=

25 cos2 x+sin2x+sin2x=

-1+25 cos2 x+sin2x=

24 cos2x-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?

4. ## Re: Hellooo/ Math problem

Hello, MathChick!

I tried to do this:

(5 cos x-sin x)2 = A cos 2x + B sin 2x+ C

25 cos2x - sin2x + sin2x . This is way off!

$\displaystyle (5\cos x - \sin x)^2$

. . $\displaystyle =\;25\cos^2\!x - 10\sin x\cos x + \sin^2\!x$

. . $\displaystyle =\;25\cos^2\!x - 5(2\sin x\cos x) + \sin^2\!x$

. . $\displaystyle =\;25\cos^2\!x - 5\sin2x + \sin^2\!x$

. . . . . . . . . . etc. . . .

5. ## Re: Hellooo/ Math problem

Oh my god!! Now I understand, thank you very much!