Discussion Forum

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

Answer:

Explanation:

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