Hi! Can someone help check this for me and see if I'm doing it right? Thanks!! :)

Directions: Use the Half-Angle formulas to determine the exact value of sin(pi/12). Here's what I have:

π/12 = ( 180° ) / 12 = 15°.

= sin ( π/12 )

= sin 15°

= sin ( 45° - 30°)

= sin 45°· cos 30° - cos 45°· sin 30°

= (1/√2)·(√3 /2 ) - (1/√2)·(1/2)

= ( √3 - 1 ) / (2√2)

2 answers

Even though you got the correct answer you did not follow the required method.
(That's like winning a 100 m backstroke race by using the butterfly stroke , you would be DQ'd)

It said to use the Half-Angle formula
There are two,
sin (2A) = 2sinAcosA
and
cos(2A) = cos^2 A - sin^2 A = 1 - 2sin^2 A = 2cos^2 A - 1

I will use
cos(2A) = 1 - 2sin^2 A
cos 30° = 1 - 2sin^2 15°
2 sin^2 15 = 1 - √3/2 = (2-√3)/2
sin^2 15 = (2 - √3)/4
sin 15 = √(2 - √3) /2

Check: by using your calculator to find sin15 , and evealutationg my answer to show they are equal

even though this answer looks different from yours, use your calculator to show that it is the same as your answer
I interpret the instruction to use the Half-Angle formula as

sin(15°) = √((1-cos30°)/2)
= √((1-√3/2)/2
= √(2-√3)/2
= (√6-√2)/2

Granted, the half- and double-angle formulas are two sides of the same coin, but ...