# What does #cos(arctan((3pi)/2))-2sin(arcsec(pi/4)) # equal?

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[ \cos(\arctan(\frac{3\pi}{2})) - 2\sin(\operatorname{arcsec}(\frac{\pi}{4})) ]

The value of ( \cos(\arctan(\frac{3\pi}{2})) ) is not defined because the arctan function returns values in the range ( -\frac{\pi}{2} < \arctan(x) < \frac{\pi}{2} ), and ( \frac{3\pi}{2} ) is outside of this range. Similarly, ( \operatorname{arcsec}(\frac{\pi}{4}) ) is not defined because the arcsec function is defined only for values greater than or equal to 1, and ( \frac{\pi}{4} ) is less than 1.

Therefore, the expression is undefined.

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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.

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