Sin 2-18-sin 2-9-sin 27-18-sin 24-9-k- Find the value of k-

nbsp;sin ^ 2 π nbsp;/ 18 nbsp; +sin ^ 2 π nbsp;/ 9 nbsp; +sin ^ 2 7π nbsp;/ 18 nbsp; +sin ^ 2 4π nbsp;/ 9 nbsp; nbsp; =sin ...

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Integration by Parts

sin 2π/18+sin...

Question

${sin}^{2} \frac{π}{18} + {sin}^{2} \frac{π}{9} + {sin}^{2} \frac{7 π}{18} + {sin}^{2} \frac{4 π}{9} = k$ . Find the value of $k$ .

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Solution

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Prove that: $s i n^{2} \frac{π}{18} + s i n^{2} \frac{π}{9} + s i n^{2} \frac{7 π}{18} + s i n^{2} \frac{4 π}{9} = 2$

$s i n^{2} \frac{π}{18} + s i n^{2} \frac{π}{9} + s i n^{2} \frac{7 π}{18} + s i n^{2} 4 \frac{π}{9} =$

The value of $s i n^{2} (\frac{π}{18}) + s i n^{2} (\frac{π}{9}) + s i n^{2} (\frac{7 π}{18}) + s i n^{2} (\frac{4 π}{9})$ is

{sin}^{2} \frac{π}{18} + {sin}^{2} \frac{2 π}{18} + {sin}^{2} \frac{4 π}{18} + {cos}^{2} \frac{π}{18} + {cos}^{2} \frac{2 π}{18} + {cos}^{2} \frac{4 π}{18}

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