Use a product-to-sum formula to convert the expression to a sum or difference. Simplify where possible. $\sin 125 ^ { \circ } \sin 5 ^ { \circ }$
A) $\frac { 1 } { 2 } \sin 130 ^ { \circ } - \frac { \sqrt { 3 } } { 4 }$
B) $- \frac { 1 } { 4 } - \frac { 1 } { 2 } \cos 130 ^ { \circ }$
C) $\frac { 1 } { 2 } \sin 130 ^ { \circ } + \frac { \sqrt { 3 } } { 4 }$
D) $\sqrt { 3 } \cos 65 ^ { \circ }$
E) $\frac { 1 } { 2 } \cos 130 ^ { \circ } - \frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

Using the product-to-sum formula, we have:

$$\sin 125^\circ \sin 5^\circ = \frac{1}{2}\left(\cos(125^\circ-5^\circ)-\cos(125^\circ+5^\circ)\right)$$

Simplifying, we get:

$$\sin 125^\circ \sin 5^\circ = -\frac{1}{4}-\frac{1}{2}\cos 130^\circ$$

So the answer is choice B.

Use a Product-To-Sum Formula to Convert the Expression to a Sum