Question

How do you use product to sum formulas to write the product `cos(pi/6)sin(pi/6)` as a sum or difference?

Answer 1

`sqrt3/4`

Explanation:

Using the `color(blue)"product to sum identity"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(cosAsinB=1/2[sin(A+B)-sin(A-B)])color(white)(2/2)|))`

`"here " A=B=pi/6`

`=1/2[sin(pi/3)-sin(0)]`

`• sin(pi/3)=sqrt3/2" and " sin(0)=0`

`rArr1/2[sqrt3/2-0]`

`=sqrt3/4`