if cos¶=x/y show that 1-tan^2¶=2x^2-y^2/x^2
asked Sep 24, 2016 in Trigonometry Answers by anonymous

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1 Answer

cos(A)=x/y. (A represents any angle ¶.)


2-1/cos^2(A)=2-y^2/x^2=(2x^2-y^2)/x^2 QED.

Another way to solve it is to use cosine=(adjacent)/(hypotenuse), so x=adjacent and y=hypotenuse. Therefore, by Pythagoras, opposite=√(y^2-x^2). Tangent=(opposite)/(adjacent)=√(y^2-x^2)/x.


answered Sep 24, 2016 by Rod Top Rated User (429,320 points)
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