Simplified Expression: Cos(a/u)/a + c

(1/. a)arcsec(u/. a)+c =

To simplify the expression (1/a)arcsec(u/a)+c, let’s break it down into its components and work with them separately

To simplify the expression (1/a)arcsec(u/a)+c, let’s break it down into its components and work with them separately.

First, consider the term (1/a)arcsec(u/a). The arcsec function is the inverse of the sec function, so we can rewrite it as sec^(-1)(u/a). Remember that sec(x) = 1/cos(x), therefore sec^(-1)(u/a) = cos^(-1)(a/u).

Now we have (1/a)cos^(-1)(a/u) + c.

Next, we can simplify the expression further. Recall that cos^(-1)(x) represents the inverse cosine function, which returns an angle whose cosine is x. Therefore, cos^(-1)(a/u) represents an angle whose cosine is a/u.

Using the identity cos^(-1)(x) = acos(x), we can rewrite the expression as (1/a)acos(a/u) + c.

Now, we can simplify this even more. The cosine function has a reciprocal relationship with the secant function, which means that cos(x) = 1/sec(x). Applying this to our expression, we can rewrite it as (1/a)(1/sec(a/u)) + c.

Recall that sec(x) = 1/cos(x), so (1/a)(1/sec(a/u)) can be simplified to (1/a)(cos(a/u)) + c.

Finally, we can simplify the expression to cos(a/u)/a + c. This is the simplified form of (1/a)arcsec(u/a) + c.

Keep in mind that this is the simplified expression based on the provided equation. If there are any other constraints or additional information given, the expression might be further simplified or manipulated accordingly.

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