Simplify the expression algebraically.
$\sin ( 7 x + 7 y ) + \sin ( 7 x - 7 y )$
A) $\sin \left( 7 x ^ { 2 } + 7 y ^ { 2 } \right)$
B) $2 \sin 7 x$
C) $\sin \left( 7 x ^ { 2 } - 7 y ^ { 2 } \right)$
D) $\sin 7 x \cos 7 y$
E) $2 \sin 7 x \cos 7 y$

Question

Simplify the expression algebraically. 
 $\sin ( 7 x + 7 y ) + \sin ( 7 x - 7 y )$  
A) $\sin \left( 7 x ^ { 2 } + 7 y ^ { 2 } \right)$
B) $2 \sin 7 x$
C) $\sin \left( 7 x ^ { 2 } - 7 y ^ { 2 } \right)$
D) $\sin 7 x \cos 7 y$
E) $2 \sin 7 x \cos 7 y$

Quizplus · Accepted Answer

Using the trigonometric identity $\sin(A + B) + \sin(A - B) = 2 \sin A \cos B$, the expression simplifies to $2 \sin 7x \cos 7y$.

Simplify the Expression Algebraically sin⁡(7x+7y)+sin⁡(7x−7y)\sin ( 7 x + 7 y ) + \sin ( 7 x - 7 y )sin(7x+7y)+sin(7x−7y)

Simplify the Expression Algebraically $\sin ( 7 x + 7 y ) + \sin ( 7 x - 7 y )$