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Trigonometric Ratios of Multiples of an Angle

cos2π10+ cos2...

Question

${cos}^{2} \frac{π}{10} + {cos}^{2} \frac{2 π}{5} + {cos}^{2} \frac{π}{5} + {cos}^{2} \frac{π}{10} =$

A

1

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B

2

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C

4

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D

6

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Solution

The correct option is A $1$
${cos}^{2} (\frac{π}{10}) + {cos}^{2} (\frac{2 π}{5}) + {cos}^{2} (\frac{π}{5}) + {cos}^{2} (\frac{π}{10})$
${cos}^{2} (\frac{π}{2} - \frac{π}{10}) + {cos}^{2} (\frac{2 π}{5}) + {cos}^{2} (\frac{π}{2} - \frac{2 π}{5}) + {cos}^{2} (\frac{π}{10})$
${sin}^{2} (\frac{2 π}{5}) + {cos}^{2} (\frac{2 π}{5}) + {sin}^{2} (\frac{π}{10}) + {cos}^{2} (\frac{π}{10})$
$1 + 1 \Rightarrow 2$
$[∵ {sin}^{2} θ + {cos}^{2} θ = 1]$ .

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Similar questions

Q. prove the following

{cos}^{2} (\frac{π}{10}) + {cos}^{2} (\frac{2 π}{5}) + {cos}^{2} (\frac{3 π}{5}) + {cos}^{2} (\frac{9 π}{10}) = 2

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