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Stuind ca ctg x=4 ,sa se calculeze ctg 2x

Răspuns :


ctg x=4 ⇔ cosx/sinx = 4

ctg2x = cos2x/sin2x =(cos²x - sin²x)/2sinx cosx = cos²x/
2sinx cosx -

- sin²x/
2sinx cosx = 1/2(cosx/sinx - sinx/cosx) =1/2(4 - 1/4) =

=(1/2)·(15/4) = 15/8.