solve using double angle idenity sin22.5cos22.5

Question

i couldnt solve the question im very confused, please help!

the directions are "use a double-angle identity to find the exact value"

Answer 1

 

Let A=22.5

cos45 = 1- 

1/√2  = 1-  

 = 

 =  

 sin22.5  =  Ans.

 

Answer 2

sin22.5cos22.5 is half a double angle

therefore a full double angle is 2sinAcosA

Thus, we sub it in as
 

1/2 (2sin22.5cos22.5)

1/2 (sin45)

1/2 (1/√2)

1/2√2... rationalise

Answer is √2/4