Question

Use the product to sum formula to help me solve this problem in trig

Answer 1

Step-by-step explanation

The product-to-sum formula can be seen below.

`cosAsinB=(1)/(2)(sin(A+B)-sin(A-B))`

Therefore, we can insert the values of the angles into the formula

`\begin{gathered} Cos37.5sin7.5=(1)/(2)(sin(37.5+7.5)-sin(37.5-7.5)) \\ =(1)/(2)(sin45-sin30) \\ =(1)/(2)((√(2))/(2)-(1)/(2)) \\ =((√(2))/(4)-(1)/(4)) \\ =(√(2)-1)/(4) \end{gathered}`

Answer:

`\begin{gathered} A=2 \\ B=1 \end{gathered}`