Express the sum or difference as a product of sines and/or cosines.
-$$\cos \frac { 5 \theta } { 2 } + \cos \frac { 3 \theta } { 2 }$$
A) $2 \sin ( 2 \theta ) \sin \theta$
B) $2 \cos ( 2 \theta ) \cos \frac { \theta } { 2 }$
C) $2 \sin ( 2 \theta ) \sin \frac { \theta } { 2 }$
D) $2 \cos ( 2 \theta )$

Question

Quizplus · Accepted Answer

The given expression can be simplified using the cosine sum formula: $\cos A + \cos B = 2 \cos \left(\frac{A + B}{2}\right) \cos \left(\frac{A - B}{2}\right)$. Applying this to the given expression, we get $2 \cos \left(\frac{5\theta}{2} + \frac{3\theta}{2}\right) \cos \left(\frac{5\theta}{2} - \frac{3\theta}{2}\right) = 2 \cos (2\theta) \cos \left(\frac{\theta}{2}\right)$.

Express the Sum or Difference as a Product of Sines cos⁡5θ2+cos⁡3θ2\cos \frac { 5 \theta } { 2 } + \cos \frac { 3 \theta } { 2 }cos25θ​+cos23θ​

Express the Sum or Difference as a Product of Sines $\cos \frac { 5 \theta } { 2 } + \cos \frac { 3 \theta } { 2 }$