Aptitude Question ID : 94464

\sin ^{2}5^{\circ}+\sin ^{2}10^{\circ}+\sin ^{2}15^{\circ}+......+\sin ^{2}85^{\circ}+\sin ^{2}90^{\circ} is equal to :
[A]7\frac{1}{2}
[B]8\frac{1}{2}
[C]9\frac{1}{2}
[D]9

\mathbf{9\frac{1}{2}}
\sin \Theta = \cos\Theta (90^{\circ}-\Theta);
\sin (90^{\circ}-\Theta) = \cos\Theta
\therefore \sin 85^{\circ} = \sin (90^{\circ}-5^{\circ}) = \cos5^{\circ}
\mathbf{\therefore (\sin^{2}5^{\circ}+\sin^{2}85^{\circ})+(\sin^{2}10^{\circ}+\sin^{2}80^{\circ})+.... to 8 terms +(\sin^{2}45^{\circ}+\sin^{2}90^{\circ})}
= 8\times 1 + \frac{1}{2}+1 = 9\frac{1}{2}
Hence option [C] is correct answer.

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