Express as a sum or difference. $\sin 7 t \sin 2 t$
A) $\cos ( 5 t ) - \cos ( 9 t )$
B) $\frac { 1 } { 2 } \cos ( 6 t ) - \frac { 1 } { 2 } \cos ( 10 t )$
C) $\sin ( 5 t ) - \sin ( 9 t )$
D) $\frac { 1 } { 2 } \cos ( 5 t ) - \frac { 1 } { 2 } \cos ( 9 t )$
E) $\frac { 1 } { 2 } \sin ( 5 t ) - \frac { 1 } { 2 } \sin ( 9 t )$

Question

Quizplus · Accepted Answer

The product-to-sum identity for sine functions is $\sin A \sin B = \frac{1}{2} [\cos(A-B) - \cos(A+B)]$. Applying this to $\sin 7t \sin 2t$, we get $\frac{1}{2} [\cos(7t-2t) - \cos(7t+2t)] = \frac{1}{2} [\cos(5t) - \cos(9t)]$.

Express as a Sum or Difference sin⁡7tsin⁡2t\sin 7 t \sin 2 tsin7tsin2t

Express as a Sum or Difference $\sin 7 t \sin 2 t$