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June 11th, 2010, 07:45 AM   #1
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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(a-b)


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(a-b) = 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
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June 11th, 2010, 08:57 AM   #2
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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.
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June 11th, 2010, 09:03 AM   #3
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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
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June 12th, 2010, 10:16 AM   #4
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Re: Derivative with a range constraint

I don't see it either.



so

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