Question -
Answer -
Let us consider LHS:
sin2 2π/5 – sin2 π/3 =sin2 (π/2 – π/10) – sin2 π/3
we know, sin (90°– A) = cos A
So, sin2 (π/2 – π/10) = cos2 π/10
Sin π/3 = √3/2
Then the above equation becomes,
= Cos2 π/10 – (√3/2)2
We know, cos π/10 = √(10+2√5)/4
the above equation becomes,
= [√(10+2√5)/4]2 – 3/4
= [10 + 2√5]/16 – 3/4
= [10 + 2√5 – 12]/16
= [2√5 – 2]/16
= [√5 – 1]/8
= RHS
Hence proved.