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tAn^2x=sEC^2x%1 Ϊʲô

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¥ԭʽ1+tan^2xɻΪ

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

⣺ tan²x=sin²x/cos²x=(1-cos²x)/cos²x=1/cos²x-1=sec²x-1 Ϊsecx=1/cosx

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

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

(tan2x + sec2x)² dx = (tan²2x + 2sec2xtan2x + sec²2x) dx = (1/2) (sec²2x - 1 + 2sec2xta2x + sec²2x) d(2x) = (1/2)(2tan2x - 2x + 2sec2x) + C = tan2x + sec2x - x + C

tan²x/(1-sin²x) dx =tan²x/cos²x dx =tan²x*sec²x dx =tan²x d(tanx) =(1/3)tan³x + C

=1/cos2x+sin2x/cosx =sec2x+tan2x=ұ ֤

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