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${cos}^{2} 9^{0} {+ cos}^{2} 18^{0} {+ cos}^{2} 27^{0} + ....... {+ cos}^{2} 81^{0} =$

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$\frac{9}{2}$

$\frac{11}{2}$

answer is B.

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Detailed Solution

$\cos^{2} 9^{0} + \cos^{2} 18^{0} + \cos^{2} 27^{0} + \cos^{2} 36^{0} + \cos^{2} 45^{0} + \cos^{2} 54^{0} + \cos^{2} 63^{0} + \cos^{2} 72^{0} + \cos^{2} 81^{0}$

$(if A + B = 90^{0} then \cos^{2} A + c o s^{2} B = 1)$

$= 4 + \frac{1}{2} = \frac{9}{2}$

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