Value of Σ_{r-1}^{18} cos^2(5r)^o, where x^o denotes x degree, is equals to

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3.Trigonometrical Ratios, Functions and Identities

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The value of $\sum_{r-1}^{18} cos^2(5r)^o,$ where $x^o $ denotes the $x$ degree, is equals to

A

$\frac{19}{2}$

B

$\frac{7}{2}$

C

$\frac{17}{2}$

D

$0$

Solution

$=\cos ^{2} 5^{\circ}+\cos ^{2} 10^{\circ}+\ldots+\cos ^{2} 85^{\circ}+\cos ^{2} 90^{\circ}$

$=8+\frac{1}{2}=\frac{17}{2}$

Standard 11

Mathematics

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(KVPY-2012)