Help with Trigonometric Simplifying

[chrisdapos]

Hi, i need help with simplifying this problem. I think it is an identity, but it looks very complex, and I wanted some other peoples thoughts/opinions. Well here goes...
cos^2((pi/4)-(x-2)) - sin^2((pi/4)-(x-2))
I reduced it using the identity cos2x=cos^2x - sin^2x. I came out with cos2((pi/4)-(x/2)), is that it? Am I looking too far into this, or is there more? Thank you so much in advance!

 

[Dale]

Don't forget your difference of angles identities. Those should allow you to split up the (pi/4) and the (x/2) terms. Then you know the sin and cos of pi/4 so those are just numbers. Then you should only be left with the (x/2) terms which you may be able to further simplify with the half angle identites.

-Dale

 

[chrisdapos]

thank you, my question would be do the addition identities apply to terms if they are squared? Do I use the same idetity regardless of wheter sin and cos are squared?

 

[Dale]

Didn't you already get rid of the squares with the cos(2x) identity?

But, in any case, you can use the addition identities and then square the results as appropriate if you want.

-Dale

 

[chrisdapos]

I reduced it down to root 2 cos^2x+root2sinxcosx...do you know if this is right or not?

 

[chrisdapos]

discard the previous responce...i reduced it to sinx...any posibility that this is right? It seems right. Thank you

 

[Dale]

Mathematica only simplified it to
$$\sin (2\,\left( -2 + x \right) )$$

Sometimes Mathematica does not actually get the simplest result. You should check by plugging in a few test values and see if your answer matches the original.

-Dale