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ǰλãҳ >> sEC2x%tAn2x=1?Ϊʲô? >>

sEC2x%tAn2x=1?Ϊʲô?

Ϊ sec²x-tan²x =1/cos²x-sin²x/cos²x =(1-sin²x)/cos²x =1

ϸдֽ

tanx = sinx/cosx (tanx)^2 = (sinx)^2/(cosx)^2 =(1- (cosx)^2 )/(cosx)^2 = 1/(cosx)^2 -1 =(secx)^2 -1

=1/cos2x+sin2x/cosx =sec2x+tan2x=ұ ֤

8

f(x) = 1 g(x) = (secx)^2 - (tanx)^2 һ, ͬ ǰ x (-, +) , x k+/2, k Ϊ

f(x)1,g(x)sec²xtan²xͬ f(x)1ԱȡֵΧʵ g(x)sec²xtan²xУX0X٦/2

y=sec2x y'=sec2x*tan2x*2=2sec2xtan2x y''=2(sec2x)'tan2x+2sec2x(tan2x)' =2sec2xtan2x*2tan2x+2sec2x*sex^2x*2 =4tan^2 2xsec2x+4sec^32x =4(sec^2 2x-1)sec2x+4sec^3 2x =8sec^3 2x-4sec2x.

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