Choose the one alternative that best completes the statement or answers the question.
Complete the identity.
-$\sin ( 4 \theta ) \sin ( 7 \theta ) \cos ( 4 \theta ) \cos ( 7 \theta ) = ?$
A) $\cos ^ { 2 } ( 56 \theta )$
B) $\frac { \sin ^ { 2 } ( 56 \theta ) } { 4 }$
C) $\frac { \cos ^ { 2 } ( 11 \theta ) + \cos ^ { 2 } ( 3 \theta ) } { 4 }$
D) $\frac { \cos ^ { 2 } ( 3 \theta ) - \cos ^ { 2 } ( 11 \theta ) } { 4 }$

Question

Quizplus · Accepted Answer

This identity can be simplified using trigonometric identities. First, recognize that the expression can be rewritten using the product-to-sum identities. The correct simplification leads to the expression $\frac { \cos ^ { 2 } ( 3 \theta ) - \cos ^ { 2 } ( 11 \theta ) } { 4 }$, which matches option D.

Choose the One Alternative That Best Completes the Statement or Answers