sin2 7˚ + sin2 9˚ + sin2 11˚ + sin2 12˚ + ……… + sin2 83˚ = ?
sin 27˚ + sin 29˚ + sin 211˚ + sin 212˚ + ……… + sin 283˚ = (sin2 7˚ + sin2 83˚)+(sin2 9˚ + sin2 81˚) + .…. + (sin2 43˚ + sin2 47˚) + sin2 45˚ = (sin2 7˚ + cos2 7˚) + (sin2 9˚ + cos2 9˚) + .…. + (sin2 43˚ + cos243˚) + sin2 45˚ {As sin (90˚ - θ) = cos θ} = (1)+(1) + .…. upto 19 times + sin2 45˚ { Assin 2θ +cos 2θ= 1} = 19 + sin2 45˚ {As there are 19 odd numbers from 7 to 43}. = 19 + (1/√2)2 {As sin 45˚ =1/√2 } = 19 + 0.5 = 19.5 ` ` ` ` ` ` ` ` ` ` ` `
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