Key to "What is the value of cosπ8?"

esterificslo1

Answered question

2023-02-26

What is the value of

\cos (\frac{π}{8})

Answer & Explanation

placerdeleermvau

Beginner2023-02-27Added 7 answers

Find the value of

\cos (\frac{π}{8})

.
In the formula

\cos 2 A = 2 \cos^{2} A - 1

,put

A = \frac{π}{8}

\cos (2 (\frac{π}{8})) = 2 \cos^{2} (\frac{π}{8}) - 1 \Rightarrow \cos (\frac{π}{4}) = 2 \cos^{2} (\frac{π}{8}) - 1 \Rightarrow \frac{1}{2} = 2 \cos^{2} (\frac{π}{8}) - 1 [∵ c o s \frac{π}{4} = c o s 45 ° = \frac{1}{2}] \Rightarrow \cos^{2} (\frac{π}{8}) = \frac{1 + \frac{1}{2}}{2} \Rightarrow \cos^{2} (\frac{π}{8}) = \frac{2 + 1}{22} \Rightarrow \cos (\frac{π}{8}) = \frac{2 + 1}{22}

Now explain the expression above.

\cos \frac{π}{8} = \frac{2 + 1}{22} \times \frac{2}{2} \Rightarrow = \frac{2 + 2}{4} \Rightarrow = \frac{2}{+}

Therefore, the value of

\cos (\frac{π}{8})

\frac{2}{+}

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