Question
sin2 7Λ + sin2 9Λ +
sin2 11Λ + sin2 12Λ + ……… + sin2 83Λ = ?Solution
sin 2 7Λ + sin 2 9Λ + sin 2 11Λ + sin 2 12Λ + ……… + sin 2 83Λ = (sin2 7Λ + sin2 83Λ)+(sin2 9Λ + sin2 81Λ) + .…. + (sin2 43Λ + sin2 47Λ) + sin2 45Λ = (sin2 7Λ + cos2 7Λ) + (sin2 9Λ + cos2 9Λ) + .…. + (sin2 43Λ + cos2 43Λ) + sin2 45Λ {As sin (90Λ - θ) = cos θ} = (1)+(1) + .…. upto 19 times + sin2 45Λ { As sin 2 θ + cos 2 θ= 1} = 19 + sin2 45Λ {As there are 19 odd numbers from 7 to 43}. = 19 + (1/√2)2 {As sin 45Λ =1/√2 } = 19 + 0.5 = 19.5 ` ` ` ` ` ` ` ` ` ` ` `
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