Finding Exact Value of Cos A: Solutions Requested

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To find the exact value of cos A from the equation sec A - cos A = 1/2, substitute cos A with x, leading to the equation (1/x) - x = 1/2. Multiply through by cos A to eliminate the fraction, resulting in a quadratic equation: 0 = cos^2 A + 0.5 cos A - 1. This can be solved using the quadratic formula to find the values of cos A. The solution provides the exact values needed for angle A.
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i and the rest of my class are finding it impossible to find the answer to this part of the question:

find the exact value of cos A from secA-cosA=1/2

thanks in advance
 
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Make the substitution \cos A =x, then the definition of secant and in the end you should get a quadratic equation in "x".

Daniel.
 
What you do is that you multiply everything by cosA, so that you get a quadratic, and then solve that in terms of cosA, to get A, simply inverse cos it, eg

(1/cosA) - cosA = 1/2
-cos^2A + 1 = (1/2)cosA
0 = cos^2A + 0.5cosA -1
Then solve with the quadratic formula:biggrin:

edit: dam,beaten to it...
 
merci beaucoup
 

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