Question
sin2 17˚ + sin2 19˚ +
sin2 21˚ + sin2 23˚ + ……… + sin2 77˚ = ?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 ` ` ` ` ` ` ` ` ` ` ` `
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