Mathematics | TS EAMCET 2019 | Discussion Page

$\sin ^{2} (3^{0})+\sin ^{2} (6^{0})+\sin ^{2} (9^{0})+....+\sin ^{2} (84^{0})+\sin ^{2} (87^{0})+\sin ^{2} (90^{0})=$

$\frac{31}{2}$

$\frac{39}{2}$

$\frac{59}{2}$

D) 36

Option A

We have,

$\sin ^{2} (3^{0})+\sin ^{2} (6^{0})+\sin ^{2} (9^{0})+....+\sin ^{2} (84^{0})+\sin ^{2} (87^{0})+\sin ^{2} (90^{0})$

= $\sin ^{2} (3^{0})+\sin ^{2} (87^{0})+\sin ^{2} (6^{0})+\sin ^{2} (84^{0})+...........\sin ^{2} (90^{0})=$

=1+1+1+.... 15 times + $\left(\frac{1}{\sqrt{2}}\right)^{2}=15+\frac{1}{2}=\frac{31}{2}$

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