Determining compositions of trig functions by knowing Euler's identity etc – math.stackexchange.com

Determining compositions of trig functions by knowing Euler's identity etc – math.stackexchange.com

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How does one determine: $$\cos^2(\arctan(x))?$$ I know what it is equal to, since its in the tables. But without working with many trigonometric identities, its not clear how to find such things. ...

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