# Thread: trig help for vector calc class

1. ## trig help for vector calc class

A’= A(cosx)^2 + 2Bcosxsinx + C(sinx)^2
C’= A(sinx)^2 – 2Bcosxsinx + C(cosx)^2

I need to prove that (A’)(C’) is equal to AC – B^2

If tried multiplying both together but I cant seem to find the right trig identities or how to simplify it.
any steps or hints would be Great

2. Originally Posted by lauren2988
A’= A(cosx)^2 + 2Bcosxsinx + C(sinx)^2
C’= A(sinx)^2 – 2Bcosxsinx + C(cosx)^2

I need to prove that (A’)(C’) is equal to AC – B^2

If tried multiplying both together but I cant seem to find the right trig identities or how to simplify it.
any steps or hints would be Great
I believe that there is something missing here, and that the correct identity should be $\displaystyle A'C'-B'^2 = AC-B^2$, where $\displaystyle B' = -A\sin x\cos x + B(\cos^2x-\sin^2x) + C\sin x\cos x$.

To prove it, check that $\displaystyle \begin{bmatrix}A'&B'\\B'&C'\end{bmatrix} = \begin{bmatrix}\phantom{-}\cos x&\sin x\\-\sin x&\cos x\end{bmatrix} \begin{bmatrix}A&B\\B&C\end{bmatrix} \begin{bmatrix}\cos x&-\sin x\\\sin x&\phantom{-}\cos x\end{bmatrix}$, and take the determinant of both sides.