PreCalc
posted by Jack .
Prove: 2  sec^x / 1+ tan ^x = cos 2x

I assume you mean
(2sec^2 x)/(1+tan^2 x)
since sec^2 x = 1+tan^2 x, we have
(1tan^2 x)/(sec^2 x)
multiply top and bottom by cos^2 x
= (cos^2 x  sin^2 x)/1
= cos(2x)
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