I know the half angle formula should be used, but I don t see how that helps with 3pi/16.
4 Answers

Nah, that's just the right side of the cosine of a sum:
cos (a+b) = (cos a)(cos b)  (sin a)(sin b)
....with a=3pi/16 and b=pi/16. the result (the left side) is:
cos (3pi/16 + pi/16) = cos (pi/4) = 1/√2

We should recognize that this is the the cosine addition identity, cos(x + y) = cos(x)cos(y)  sin(x)sin(y)
cos(3pi/16)cos(pi/16)  sin(3pi/16)sin(pi/16)
=cos(3pi/16 + pi/16)
=cos(4pi/16)
=cos(pi/4)
=1/√2

cos(3pi/16)cos(pi/16)  sin(3pi/16)sin(pi/16)
=cos A cosB  sinA sinB [Say , A=3pi/16, B=pi/16 ]
=cos(A+B)
=Cos{(3pi/16)+(pi/16)}
=cos(4pi/16)
=cos (pi/4)
=cos 45 deg
=1 / sqrt2

cos(a + b) = cosa cosb  sina sinb
cos(3π/16 + π/16) = cos(π/4) = √(2)/2