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

Answer 1

#color (red)(sqrt3/2)#

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

#sqrt3/2#

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

The above expression simplifies to

#cos (2pi/9 - pi/18)# #cos (3pi/18)#
#cos (pi /6) = cos 30 = sqrt3/2#
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Answer 3

You can use the cosine of the difference formula ( \cos(A - B) = \cos A \cos B + \sin A \sin B ) to find the exact value of ( \cos\left(\frac{2\pi}{9}\right) \cos\left(\frac{\pi}{18}\right) + \sin\left(\frac{2\pi}{9}\right) \sin\left(\frac{\pi}{18}\right) ).

Using the given angles ( \frac{2\pi}{9} ) and ( \frac{\pi}{18} ):

[ \cos\left(\frac{2\pi}{9} - \frac{\pi}{18}\right) ]

[ = \cos\left(\frac{4\pi}{18} - \frac{\pi}{18}\right) ]

[ = \cos\left(\frac{3\pi}{18}\right) ]

[ = \cos\left(\frac{\pi}{6}\right) ]

[ = \frac{\sqrt{3}}{2} ]

So, the exact value is ( \frac{\sqrt{3}}{2} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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