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Expert: Scotto - 7/2/2008


Question
please give me the proof of the equation Cos2X+Cos2Y+Cos2Z=1


Answer
This is just like a three dimensional triangle.

The Pythagorean theorem states that a²+b²=c² when in two dimensions.  Divide the entire equation by the variable c to get
(a/c)²+(b/c)²=1.  Note that a/c=cos(t) and b/c=cos(u) where u and t are the two angles in the triangle.
The equation is then cos²(t)+cos²(u)=1 for all u,t where u+t=90.

Take a three dimesional box with sides w, l, and h.
The diagonal across the bottom²=w²+l².  This diagonal line we will call d.  It is alson known that d²+h²=c² where c is the line across the recangular box from the lower corner to the opposite top corner.  
We know that d²=w²+l², so putting this in gives w²+l²+j²=c².  Divide the entire equation by c² and you will get the equation given.  That is, the sum of cos² of each of the angles is 1.

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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