- #1
Gekko
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Homework Statement
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)
The Attempt at a Solution
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 I've been totally stumped on this and the equality is required further on