Question -
Answer -
Let us consider LHS:
sin2 π/18 + sin2 π/9 +sin2 7π/18 + sin2 4π/9
sin2 π/18 + sin2 2π/18+ sin2 7π/18 + sin2 8π/18
sin2 π/18 + sin2 2π/18+ sin2 (π/2 – 2π/18) + sin2 (π/2 – π/18)
We know that when n is odd, sin → cos.
sin2 π/18 + sin2 2π/18+ cos2 2π/18 + cos2 2π/18
when rearranged,
sin2 π/18 + cos2 2π/18+ sin2 π/18 + cos2 2π/18
We know that sin2 + cos2x =1.
So,
1 + 1
2 = RHS
∴ LHS = RHS
Hence proved.