Aptitude Question ID : 94464
$latex \sin ^{2}5^{\circ}+\sin ^{2}10^{\circ}+\sin ^{2}15^{\circ}+……+\sin ^{2}85^{\circ}+\sin ^{2}90^{\circ}$ is equal to :
[A]$latex 7\frac{1}{2}&s=1$
[B]$latex 8\frac{1}{2}&s=1$
[C]$latex 9\frac{1}{2}&s=1$
[D]$latex 9$
$latex \mathbf{9\frac{1}{2}}&s=1$
$latex \sin \Theta = \cos\Theta (90^{\circ}-\Theta);$
$latex \sin (90^{\circ}-\Theta) = \cos\Theta$
$latex \therefore \sin 85^{\circ} = \sin (90^{\circ}-5^{\circ}) = \cos5^{\circ}$
$latex \mathbf{\therefore (\sin^{2}5^{\circ}+\sin^{2}85^{\circ})+(\sin^{2}10^{\circ}+\sin^{2}80^{\circ})+…. to 8 terms +(\sin^{2}45^{\circ}+\sin^{2}90^{\circ})}$
$latex = 8\times 1 + \frac{1}{2}+1 = 9\frac{1}{2}$
Hence option [C] is correct answer.