Trigonometry Product to Sum Identities

Write the following product as a sum:

 $\sin7\beta\sin3\beta$  

•  $\frac{1}{2}\left[\sin\left(7\beta+3\beta\right)+\sin\left(7\beta-3\beta\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(7\beta+3\beta\right)-\sin\left(7\beta-3\beta\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(7\beta+3\beta\right)+\cos\left(7\beta-3\beta\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(7\beta-3\beta\right)-\cos\left(7\beta+3\beta\right)\right]$  

Write the following product as a sum:

 $\cos45\degree\cos15\degree$  

•  $\frac{1}{2}\left[\sin\left(60\degree\right)+\sin\left(30\degree\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(60\degree\right)-\sin\left(30\degree\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(60\degree\right)+\cos\left(30\degree\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(30\degree\right)-\cos\left(60\degree\right)\right]$  

Write the following product as a sum:

 $2\sin9\beta\cos3\beta$  

•  $\sin\left(12\beta\right)+\sin\left(6\beta\right)$  

•  $\sin\left(12\beta\right)-\sin\left(6\beta\right)$  

•  $\left[\cos\left(12\beta\right)+\cos\left(6\beta\right)\right]$  

•  $\cos\left(6\beta\right)-\cos\left(12\beta\right)$  

Write the following product as a sum:

 $\cos2\theta\sin2\theta$  

•  $\frac{1}{2}\left[\sin\left(4\theta\right)+\sin\left(0\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(4\theta\right)-\sin\left(0\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(4\theta\right)+\cos\left(0\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(4\theta\right)-\cos\left(0\right)\right]$  

What is the value of  $\cos45\degree$  

•  $\frac{\sqrt{2}}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{1}{2}$  

•  $1$  

Write the following product as a sum:

 $\cos2\theta-\cos8\theta$  

•  $2\sin\frac{2\theta+8\theta}{2}\cos\frac{2\theta-8\theta}{2}$  

•  $2\cos\frac{2\theta+8\theta}{2}\sin\frac{2\theta-8\theta}{2}$  

•  $2\cos\frac{2\theta+8\theta}{2}\cos\frac{2\theta-8\theta}{2}$  

•  $-2\sin\frac{2\theta+8\theta}{2}\sin\frac{2\theta-8\theta}{2}$  

Write the following product as a sum:

 $\sin3\delta+\sin\delta$  

•  $2\sin\frac{4\delta}{2}\cos\frac{2\delta}{2}$  

•  $2\cos\frac{4\delta}{2}\sin\frac{2\delta}{2}$  

•  $2\cos\frac{4\delta}{2}\cos\frac{2\delta}{2}$  

•  $-2\sin\frac{4\delta}{2}\sin\frac{2\delta}{2}$  

Write the following product as a sum:

 $\sin60-\sin45$  

•  $2\sin\frac{105}{2}\cos\frac{15}{2}$  

•  $2\cos\frac{105}{2}\sin\frac{15}{2}$  

•  $2\cos\frac{105}{2}\cos\frac{15}{2}$  

•  $-2\sin\frac{105}{2}\sin\frac{15}{2}$  

Write the following product as a sum:

 $\cos75+\cos15$  

•  $2\sin45\cos30$  

•  $2\cos45\sin30$  

•  $2\cos45\cos30$  

•  $-2\sin45\sin30$  

What is the value of  $\sin60\degree$  

•  $\frac{\sqrt{2}}{2}$  

•  $\frac{\sqrt{3}}{2}$  

•  $\frac{1}{2}$  

•  $1$