sin^{2} 7˚ + sin^{2} 9˚ + sin^{2} 11˚ + sin^{2} 12˚ + ……… + sin^{2} 83˚ = ?

sin ^{2}7˚ + sin ^{2}9˚ + sin ^{2}11˚ + sin ^{2}12˚ + ……… + sin ^{2}83˚ = (sin^{2} 7˚ + sin^{2} 83˚)+(sin^{2} 9˚ + sin^{2} 81˚) + .…. + (sin^{2} 43˚ + sin^{2} 47˚) + sin^{2} 45˚ = (sin^{2} 7˚ + cos^{2} 7˚) + (sin^{2} 9˚ + cos^{2} 9˚) + .…. + (sin^{2} 43˚ + cos^{2}43˚) + sin^{2} 45˚ {As sin (90˚ - θ) = cos θ} = (1)+(1) + .…. upto 19 times + sin^{2} 45˚ { Assin ^{2}θ +cos ^{2}θ= 1} = 19 + sin^{2} 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 ` ` ` ` ` ` ` ` ` ` ` `

Which of the following statements is / are true?

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A question and two statements labeled (I), (II) are given. You have to decide which statement(s) is/are sufficient to answer the question.

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