Show that cos(sin^(-1) v + cos^(-1) v) = 0.

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- November 12th 2008, 07:18 AM #1

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- November 12th 2008, 07:31 AM #2
Let and

First, we can rewrite using the identity

Its good to note that and [why do you think this is the case?]. So our expression can be written as

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Now let's construct two different triangles, one that has an angle and an angle

Starting with , we see that the side opposite of the angle has a value of and that the hypotenuse has a value of . Using the pythagorean theorem, we can find the value of the adjacent side:

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Now, we construct at triangle for . We see that the side adjacent of the angle has a value of and that the hypotenuse has a value of . Using the pythagorean theorem, we can find the value of the opposite side:

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Now what do you think equals?

--Chris

- November 12th 2008, 07:35 AM #3

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- November 12th 2008, 07:44 AM #4

- November 12th 2008, 04:40 PM #5

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- November 12th 2008, 04:41 PM #6

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- November 12th 2008, 06:30 PM #7