Question
Asked Jan 17, 2020
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Use the same-derivative argument to prove the identities

a. tan-1 x + cot-1 x = pai/ 2 

 b. sec-1 x + csc-1 x =pai/2.

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Expert Answer

Step 1

Recall that the mean value theorem is as follows:

Suppose f(x) is a function that satisfies both of the following.  

(a) f(x) is continuous on the closed interval [a, b].

(b) f(x) is differentiable on the open interval (a, b)  .

Then there is a number c such that a < c < b and

Calculus homework question answer, step 1, image 1
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Step 2

An extension of this theorem states that:

Calculus homework question answer, step 2, image 1
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Step 3

We will use this corollary of mean value theorem to prove the results in pa...

Calculus homework question answer, step 3, image 1
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Math

Calculus

Derivative

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