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Chain Rule of Differentiation

Solve cos2π...

Question

Solve ${cos}^{2} \frac{π}{8} + {cos}^{2} \frac{3 π}{8} + {cos}^{2} \frac{5 π}{8} + {cos}^{2} \frac{7 π}{8}$

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Solution

From question,
${cos}^{2} \frac{π}{8} + {cos}^{2} (\frac{π}{2} - \frac{π}{8}) + {cos}^{2} \frac{5 π}{8} + {cos}^{2} (\frac{3 π}{2} - \frac{5 π}{8})$

$= {cos}^{2} \frac{π}{8} + {sin}^{2} \frac{π}{8} + {cos}^{2} \frac{5 π}{8} + {sin}^{2} \frac{5 π}{8}$ ......as.. ( ${sin}^{2} θ + {cos}^{2} θ = 1$ )
$= 1 + 1$
$= 2$

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Similar questions

c o s^{2} \frac{π}{8} + c o s^{2} \frac{3 π}{8} + c o s^{2} \frac{5 π}{8} + c o s^{2} \frac{7 π}{8} = 2

Q. Prove the following identities:

{cos}^{2} \frac{π}{8} + {cos}^{2} \frac{3 π}{8} + {cos}^{2} \frac{5 π}{8} + {cos}^{2} \frac{7 π}{8} = 2

Q. Find the value of

{cos}^{2} \frac{π}{16} + {cos}^{2} \frac{3 π}{16} + {cos}^{2} \frac{5 π}{16} + {cos}^{2} \frac{7 π}{16}

Q. The value of

{cos}^{2} (\frac{π}{16}) + {cos}^{2} (\frac{3 π}{16}) + {cos}^{2} (\frac{5 π}{16}) + {cos}^{2} (\frac{7 π}{16})

Q. The value of

{cos}^{2} (\frac{π}{8} + x) - {sin}^{2} (\frac{3 π}{8} - x)

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