# How do you simplify the expression #sin (arctan (1/4) + arccos (3/4) )#?

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To simplify the expression sin (arctan (1/4) + arccos (3/4)), you can use the trigonometric identities and properties. First, find the values of arctan (1/4) and arccos (3/4).

arctan (1/4) represents the angle whose tangent is 1/4. Thus, if we take the tangent of this angle, we get 1/4. Similarly, arccos (3/4) represents the angle whose cosine is 3/4. So, if we take the cosine of this angle, we get 3/4.

Now, find the sine of the sum of these angles. You can use the sum formula for sine: sin (a + b) = sin(a)cos(b) + cos(a)sin(b).

Substitute the values of sin(arctan(1/4)), cos(arctan(1/4)), sin(arccos(3/4)), and cos(arccos(3/4)) into the formula, then calculate the expression sin(arctan(1/4) + arccos(3/4)).

Finally, simplify the expression to get the result.

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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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