How do you find the exact value of $cos (\frac{2 π}{9}) cos (\frac{π}{18}) + sin (\frac{2 π}{9}) sin (\frac{π}{18})$ $cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)$ ?

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How do you find the exact value of $cos (\frac{2 π}{9}) cos (\frac{π}{18}) + sin (\frac{2 π}{9}) sin (\frac{π}{18})$ $cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)$ ?

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Answer 1 · 2016-02-16T09:29:57

$\frac{\sqrt{3}}{2}$ $sqrt3/2$

Explanation:

This is of the form $cos (a - b) = cos (a) cos (b) + sin (a) sin (b)$ $cos(a-b)=cos (a)cos (b)+sin (a)sin (b)$

The above expression simplifies to

$cos (2 \frac{π}{9} - \frac{π}{18})$ $cos (2pi/9 - pi/18)$
$cos (3 \frac{π}{18})$ $cos (3pi/18)$

$cos (\frac{π}{6}) = cos 30 = \frac{\sqrt{3}}{2}$ $cos (pi /6) = cos 30 = sqrt3/2$

Answer 2 · 2017-12-25T16:01:50

$\frac{\sqrt{3}}{2}$ $color (red)(sqrt3/2)$

Explanation:

we know that
$cos (A - B) = cos A \times cos B + sin A \times sin B$ $color (cyan)(cos (A-B)=cosA×cosB+sinA×sinB)$
similarly the equation given is question can be written as
$cos (2 \frac{π}{9} - \frac{π}{18})$ $cos (2pi/9-pi/18)$
$cos (\frac{4 π - π}{18})$ $cos ((4pi-pi)/18)$
$cos (3 \frac{π}{18})$ $cos (3pi/18)$
$cos (\frac{π}{6})$ $cos (pi/6)$
$cos ((180°)/6)$
$color (green)(cos (30°) = sqrt3/2)$

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How do you find the exact value of $cos (\frac{2 π}{9}) cos (\frac{π}{18}) + sin (\frac{2 π}{9}) sin (\frac{π}{18})$ $cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)$ ?

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Explanation:

Explanation:

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How do you find the exact value of cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)cos(2π9)cos(π18)+sin(2π9)sin(π18)cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)?

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Explanation:

Explanation:

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How do you find the exact value of $cos (\frac{2 π}{9}) cos (\frac{π}{18}) + sin (\frac{2 π}{9}) sin (\frac{π}{18})$ $cos ((2pi)/9) cos (pi/18)+sin ((2pi)/9) sin (pi/18)$ ?