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