Question

sin^2 0+sin^2 15+sin^2 30+sin^2 45+sin^2 60+sin^2 75+sin^2 90

Answer 1

   
Folosim formulele:     sin x = cos (90 - x)   si   sin² x + cos² x = 1

   sin² 0+sin² 15+sin² 30+sin² 45+sin² 60+sin² 75+sin² 90 = 
=sin² 0+sin² 15+sin² 30+sin² 45+cos²(90 - 60)+cos²(90-75)+cos²(90-90) =
=sin² 0+sin² 15+sin² 30+sin² 45+cos² 30+cos² 15+cos² 0 =
= (sin² 0+cos² 0) + (sin² 15+cos² 15) + (sin² 30+cos² 30) + sin² 45 = 
= 1 + 1 + 1 + (√2 / 2)² = 3 + (2 / 4) = 3 + (1 / 2) = 7 / 2