Help me find the step by step answer for the exact value of 8 cos(67.5degrees)sin(22.5degrees)?

Answer 1

In a 45-45-90 triangle sin 45=cos 45 = sqrt(2)/2
sin (22.5) = sin(45/2) = +/- sqrt((1-cos45)/2)
So sin(22.5) = +/-sqrt((1-sqrt(2)/2)/2)
Now 67.5 degrees = 90 - 22.5 degrees
So cos (67.5) = sin (22.5)
So answer is 8(1-sqrt(2)/2)

Answer 2

cos(a)sin(b)=1/2(sin(a+b)-sin(a-b))

4(sin(90)-sin(45))=4(1-√2/2)