Complete the identity.
-$\sin 4 x \sin 6 x \cos 4 x \cos 6 x =$ ?
A) $\frac { \cos ^ { 2 } 2 x - \cos ^ { 2 } 10 x } { 4 }$
B) $\frac { \sin ^ { 2 } 48 x } { 4 }$
C) $\frac { \cos ^ { 2 } 10 x + \cos ^ { 2 } 2 x } { 4 }$
D) $\cos ^ { 2 } 48 x$

Question

Quizplus · Accepted Answer

This identity can be solved using the product-to-sum formulas. Specifically, we can use the formulas $\sin A \cos B = \frac{1}{2} [\sin(A+B) + \sin(A-B)]$ and $\sin A \sin B = \frac{1}{2} [\cos(A-B) - \cos(A+B)]$. Applying these formulas to $\sin 4x \cos 6x$ and $\sin 6x \cos 4x$, and then combining the results, we get an expression that simplifies to $\frac { \cos ^ { 2 } 2 x - \cos ^ { 2 } 10 x } { 4 }$.

Complete the Identity sin⁡4xsin⁡6xcos⁡4xcos⁡6x=\sin 4 x \sin 6 x \cos 4 x \cos 6 x =sin4xsin6xcos4xcos6x=

Complete the Identity $\sin 4 x \sin 6 x \cos 4 x \cos 6 x =$