Question
sin2 12˚ + sin2 14˚ +
sin2 16˚ + sin2 18˚ + ……… + sin2 78˚ =?Solution
sin 2 12˚ + sin 2 14˚ + sin 2 16˚ + sin 2 18˚ + ……… + sin 2 78˚ = (sin2 12˚ + sin2 78˚) + (sin2 14˚ + sin2 86˚) + .…. + (sin2 44˚ + sin2 46˚) = (sin2 12˚ + cos2 12˚)+(sin2 14˚ + cos2 14˚) + .…. + (sin2 44˚ + co2 44˚) {As sin (90˚ - θ) = cos θ} = (1)+(1) + .…. upto 17 times { As sin2 θ + cos2 θ= 1} = 17 ` ` ` ` ` ` ` ` ` ` ` `
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