Question

Arrange the steps in the correct order to solve:
sin 3pi/4 cos pi/12

Answer 1

`\bf \textit{Product to Sum Identities} \\\\ sin(\alpha)cos(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad +\quad sin(\alpha-\beta)]\\\\ -------------------------------\\\\ sin\left( (3\pi )/(4) \right)cos\left( (\pi )/(12) \right)\implies \cfrac{1}{2}\left[ sin\left( (3\pi )/(4)+(\pi )/(12) \right) ~~+~~sin\left( (3\pi )/(4)-(\pi )/(12) \right)\right]`


`\bf \cfrac{1}{2}\left[ sin\left( (9\pi+\pi )/(12) \right) ~~+~~sin\left( (9\pi-\pi )/(12) \right)\right] \\\\\\ \cfrac{1}{2}\left[ sin\left( (10\pi )/(12) \right) ~~+~~sin\left( (8\pi )/(12) \right)\right]\implies \cfrac{1}{2}\left[ sin\left( (5\pi )/(6) \right) ~~+~~sin\left( (2\pi )/(3) \right)\right] \\\\\\ \cfrac{1}{2}\left[\cfrac{1}{2}~~+~~\cfrac{√(3)}{2} \right]\implies \cfrac{1}{2}\left[ \cfrac{1+√(3)}{2} \right]\implies \cfrac{1+√(3)}{4}`

Answer 2

Explanation: I got it right on Edmentum.