Question

Find value of cos pi/8 find the value of
Cos pi/8

Answer 1

Answer:

The value of Cosπ/8 is...

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Answer 2

The value of $\csos\dfrac{\pi}{8}=\dfrac{\sqrt{2}(1+\sqrt{2})}{4}$  .

Explanation:

To find : $\cos (\dfrac{\pi}{8})$

Consider : $\cos (\dfrac{\pi}{4})$

$=\cos (2(\dfrac{\pi}{8}))\\\\=2\cos^2(\dfrac{\pi}{8})-1\ \ [\because \cos 2x = 2\cos^x-1]$

Since $\cos \dfrac{\pi}{4}=\dfrac{1}{\sqrt{2}}$

$\Rightarrow\ 2\cos^2(\dfrac{\pi}{8})-1=\dfrac{1}{\sqrt{2}}\\\\\Rightarrow\ 2\cos^2(\dfrac{\pi}{8})=\dfrac{1}{\sqrt{2}}+1\\\\\Rightarrow\ 2\cos^2(\dfrac{\pi}{8})=\dfrac{1+\sqrt{2}}{\sqrt{2}}\\\\\Rightarrow\ 2\cos^2(\dfrac{\pi}{8})=\dfrac{1+\sqrt{2}}{2\sqrt{2}}\times \dfrac{\sqrt{2}}{\sqrt{2}}\\\\=\dfrac{\sqrt{2}(1+\sqrt{2})}{4}$

Hence, the value of $\csos\dfrac{\pi}{8}=\dfrac{\sqrt{2}(1+\sqrt{2})}{4}$  .

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