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The value of the expression:sin<sup>2</sup>1° + sin<sup>2</sup>11° + sin<sup>2</sup>21° + sin<sup>2</sup>31° + sin<sup>2</sup>41° + sin<sup>2</sup>45° + sin<sup>2</sup>49° + sin<sup>2</sup>59° + sin<sup>2</sup>69° + sin<sup>2</sup>79° + sin<sup>2</sup>89° is?

Correct Answer: $${\text{5}}\frac{1}{2}$$
sin21° + sin211° + sin221° + sin231° + sin241° + sin245° + sin249° + sin259° + sin269° + sin279° + sin289°
= (sin21° + sin289°) + (sin211° + sin279°) + (sin221° + sin269°) + (sin231° + sin259°) + (sin241° + sin249°) + sin245°
= 1 + 1 + 1 + 1 + 1 + $$\frac{1}{2}$$  
= $$5\frac{1}{2}$$

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