June 11th, 2010, 07:45 AM  #1 
Newbie Joined: Jun 2010 Posts: 11 Thanks: 0  Derivative with a range constraint
I have the following question: x=sin(a) / cos(b) a+b < pi/2 a>0, b>0 0<x<1 show that da/dx = cos^3(b)cos(a) / cos(a+b)cos(ab) My attempt is: dx/da = cos(a) / cos(b) therefore da/dx = cos(b) / cos(a) =cos^3(b)cos(a) / cos^2(b)cos^2(a) However the denominator of the desired format = cos(a+b)cos(ab) = cos^2(a)cos^2(b)sin^2(a)sin^2(b) Not sure how to get rid of the sin^2(a)sin^2(b) term. Is the question wrong or is there something special that needs to be done to take into account the range of a, b and x? Very much appreciate help as Ive been totally stumped on this and the equality is required further on 
June 11th, 2010, 08:57 AM  #2 
Senior Member Joined: Jan 2009 Posts: 344 Thanks: 3  Re: Derivative with a range constraint
If you need to clarify/check you work/answers, there is a great http://www.wolframalpha.com/ to do this.

June 11th, 2010, 09:03 AM  #3 
Newbie Joined: Jun 2010 Posts: 11 Thanks: 0  Re: Derivative with a range constraint
Yes I know about Wolfram but that just confirms my calculation. I suspect the range isnt being taken into account but cant see where

June 12th, 2010, 10:16 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond  Re: Derivative with a range constraint
I don't see it either. so 

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constraint, derivative, range 
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