sin2 17˚ + sin2 19˚ +

Solution

sin ² 17˚ + sin ² 19˚ + sin ² 21˚ + sin ² 23˚ + ……… + sin ² 77˚   = (sin² 17˚ + sin² 73˚) + (sin² 19˚ + sin² 71˚) + .…. + (sin² 43˚ + sin² 47˚) + sin² 45˚ = (sin² 17˚ + cos² 17˚) + (sin² 19˚ + cos² 19˚) + .…. + (sin² 43˚ + cos² 43˚) + sin² 45˚  {As sin (90˚ - θ) = cos θ} = (1)+(1) + .…. upto 14 times + sin² 45˚   { As sin ² θ + cos ² θ= 1} = 14 + sin² 45˚  {As there are 14 odd numbers from 14 to 43}. = 14 + (1/√2)²  {As sin 45˚ =1/√2 } = 14 + 0.5 = 14.5 ` ` ` ` ` ` ` ` ` ` ` `