Karthik J
Last Activity: 11 Years ago
Sin2 1 + sin2 3 + ... + sin2 45 + ... + sin2 87 + sin2 89
= sin2 1 + sin2 3 + ... + 1/2 + ... + sin2 (90-3) + sin2 (90-1)
= sin2 1 + sin2 3 + ... + 1/2 + ... + cos2 87 + cos2 89
Grouping the sin2x + cos2x terms,
= (sin2 1 + cos2 1) + (sin2 3 + cos2 3) + ... + 1/2
There will be 23 such terms, which are all = 1
= 1+1+1+...23 times + 1/2
=23+1/2
=47/2