How do you express sin(pi/12) * cos(( 13 pi)/12 ) without products of trigonometric functions?

1 Answer
Jul 3, 2018

color(red)(-sin (pi/6)= -1/2

Explanation:

https://study.com/academy/lesson/product-to-sum-identities-uses-applications.htmlhttps://study.com/academy/lesson/product-to-sum-identities-uses-applications.html

sin (pi/12) * cos ((13pi)/12)

sin x cos y = (1/2)[sin(x+y) + sin (x-y])

=> (1/2)[sin (pi/12 + (13pi)/12) + sin (pi/12 - (13pi)/12)]

=> [sin ((14pi)/12) + sin (-pi)]/2

=> [sin (pi + pi/6) - sin (pi)]/2

color(red)(-sin (pi/6)= -1/2