Let us consider the 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)
As we know that when n is odd, sin → cos.
sin2 π/18 + sin2 2π/18 + cos2 2π/18 + cos2 2π/18
Let us rearrange this
sin2 π/18 + cos2 2π/18 + sin2 π/18 + cos2 2π/18
As we know that sin2 + cos2x = 1.
Therefore,
1 + 1
2 = RHS
∴ LHS = RHS
Thus, proved.
