What is the exact value of the following expression? cos (−5π/12)

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What is the exact value of the following expression? cos (−5π/12)

Use the sum and difference identities to determine the exact value.

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Answer 1 · 2018-06-05T00:46:57

$- (\frac{\sqrt{2 + \sqrt{3}}}{2})$ $-(sqrt(2 + sqrt3)/2)$

Explanation:

$cos (\frac{- 5 π}{12}) = cos (\frac{π}{12} - π) = - cos (\frac{π}{12})$ $cos ((-5pi)/12) = cos (pi/12 - pi) = - cos (pi/12)$
Find $cos (\frac{π}{12})$ $cos (pi/12)$ by using trig identity:'
$cos 2 a = 2 {cos}^{2} a - 1$ $cos 2a = 2cos^2 a - 1$ .
In this case
$cos 2 a = cos (\frac{π}{6}) = \frac{\sqrt{3}}{2}$ $cos 2a = cos (pi/6) = sqrt3/2$
$2 {cos}^{2} (\frac{π}{12}) = 1 + \frac{\sqrt{3}}{2} = \frac{2 + \sqrt{3}}{2}$ $2cos^2 (pi/12) = 1 + sqrt3/2 = (2 + sqrt3)/2$
${cos}^{2} (\frac{π}{12}) = \frac{2 + \sqrt{3}}{4}$ $cos^2 (pi/12) = (2 + sqrt3)/4$
$cos (\frac{π}{12}) = \frac{\sqrt{2 + \sqrt{3}}}{2}$ $cos (pi/12) = sqrt(2 + sqrt3)/2$ (because cos (pi/12) is positive)
Finally,
$cos (\frac{- 5 π}{12}) = - cos (\frac{π}{12}) = - \frac{\sqrt{2 + \sqrt{3}}}{2}$ $cos ((-5pi)/12) = - cos (pi/12) = - sqrt(2 + sqrt3)/2$

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What is the exact value of the following expression? cos (−5π/12)

Use the sum and difference identities to determine the exact value.

1 Answer

Explanation:

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