Question -
Answer -
Let us consider LHS:
sin2 (π/8 + x/2) – sin2 (π/8– x/2)
we know, sin2 A – sin2 B= sin (A+B) sin (A-B)
so,
sin2 (π/8 + x/2) – sin2 (π/8– x/2) = sin (π/8 + x/2 + π/8 – x/2) sin (π/8 + x/2 – (π/8 – x/2))
= sin (π/8 + π/8) sin (π/8 + x/2 – π/8 + x/2)
= sin π/4 sin x
= 1/√2 sin x [since, since π/4 = 1/√2]
= RHS
Hence proved.