Line segments joining the points (9,3) (-3,-3)

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bbanfield1

12.03.2023

Mathematics

$1 - 2\cos^2(x) = 2\sin^2(x)-1\\\\1 - 2(1-\sin^2(x)) = 2\sin^2(x)-1\\\\1 - 2+2\sin^2(x) = 2\sin^2(x)-1\\\\-1+2\sin^2(x) = 2\sin^2(x)-1\\\\2\sin^2(x)-1 = 2\sin^2(x)-1\\\\$

Notice how the right hand side stays the same the entire time. The goal is to transform one side into the other. You could transform the right side into the left side if you wanted. I used the pythagorean identity $\cos^2(x)+\sin^2(x)=1$ in which I solved for cos^2 to get $\cos^2(x)=1-\sin^2(x)$

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