Please help!!!!!!!!!!!!!!very urgent. TRIGONOMETRY

Sin2(π/8 + A/2) - Sin2(π/8 - A/2)=1/√2 sinA
NOTE: The 2 written after sin is sin square.........

Sin2(π/8 + A/2) - Sin2(π/8 - A/2)
=(Sin(π/8 + A/2) - Sin(π/8 - A/2))(Sin(π/8 + A/2) + Sin(π/8 - A/2)) [Since A^2-B^2=(A+B)(A-B)]
=(2cosπ/8.Sin A/2)(2sin π/8 . Sin A/2)
re arranging we get
(2 Sin π/8 Cosπ/8)(2 Sin A/2 Cos A/2)=Sin π/4. sin A=1/√2 sin A