Question

please answer this...​

Answer 1

Answer:

Step-by-step explanation:

$sin(A+B)=sinAcosB+cosAsinB .......1\\\\sin(A-B)=sinAcosB-cosAsinB.........2\\\\1+2\\\\=>sin(A+B)+sin(A-B)=2sinAcosB\\\\1-2\\\\=>sin(A+B)-sin(A-B)=2cosAsinB\\\\And\\\\x^2-y^2=(x+y)(x-y)\\\\Now\\Sin^2(\frac{\pi}{8}+\frac{x}{2})-Sin^2(\frac{\pi}{8}-\frac{x}{2})\\\\=(sin(\frac{\pi}{8}+\frac{x}{2})-sin(\frac{\pi}{8}-\frac{x}{2}))(sin(\frac{\pi}{8}+\frac{x}{2})-sin(\frac{\pi}{8}+\frac{x}{2}))\\\\=4sin\frac{x}{2}cos\frac{x}{2}sin\frac{\pi}{8}cos\frac{\pi}{8}\\\\=sinxsin\frac{\pi}{4}$

$=\frac{sinx}{\sqrt{2}}$

Hope it helps