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# gs - h h(tgx = sec 2 x(ctgx = csc x(sec x = sec x tgx(csc x...

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h ç · ª * ·ª ·ª* (mj a x x a a a ctgx x x tgx x x x ctgx x tgx a x x ln 1 ) (log ln ) ( csc ) (csc sec ) (sec csc ) ( sec ) ( 2 2 = = - = = - = = 2 2 2 2 1 1 ) ( 1 1 ) ( 1 1 ) (arccos 1 1 ) (arcsin x arcctgx x arctgx x x x x + - = + = - - = - = + ± + = ± + = + = + = + - = + = + - = = + = = C a x x a x dx C shx chxdx C chx shxdx C a a dx a C x ctgxdx x C x dx tgx x C ctgx xdx x dx C tgx xdx x dx x x ) ln( ln csc csc sec sec csc sin sec cos 2 2 2 2 2 2 2 2 C a x x a dx C x a x a a x a dx C a x a x a a x dx C a x arctg a x a dx C ctgx x xdx C tgx x xdx C x ctgxdx C x tgxdx + = - + - + = - + + - = - + = + + - = + + = + = + - = arcsin ln 2 1 ln 2 1 1 csc ln csc sec ln sec sin ln cos ln 2 2 2 2 2 2 2 2 + + - = - + - + - - = - + + + + + = + - = = = - C a x a x a x dx x a C a x x a a x x dx a x C a x x a a x x dx a x I n n xdx xdx I n n n n arcsin 2 2 ln 2 2 ) ln( 2 2 1 cos sin 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 0 π π

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2 2 2 2 1 2 2 1 1 cos 1 2 sin u du dx x tg u u u x u u x + = = + - = + = ( E ` ( ·ª* · ( ·ª n n A sin cos tg ctg -sinα cosα -tgα -ctgα 90°-α cosα sinα ctgα tgα 90°+α cosα -sinα -ctgα -tgα 180°-α sinα -cosα -tgα -ctgα 180°+α -sinα -cosα tgα ctgα 270°-α -cosα -sinα ctgα tgα 270°+α -cosα sinα -ctgα -tgα 360°-α -sinα cosα -tgα -ctgα 360°+α sinα cosα tgα ctgα · · { 2 sin 2 sin 2 cos cos 2 cos 2 cos 2 cos cos 2 sin 2 cos 2 sin sin 2 cos 2 sin 2 sin sin β α β α β α β α β α β α β α β α β α β α β α β α - + = - - + = + - + = - - + = + α β β α β α β α β α β α β α β α β α β α β α β α ctg ctg ctg ctg ctg tg tg tg tg tg ± = ± ± = ± = ± ± = ± 1 ) ( 1 ) ( sin sin cos cos ) cos( sin cos cos sin ) sin( x x arthx x x archx x x arshx e e e e chx shx thx e e chx e e shx x x x x x x x x - + = - + ± = + + = + - = = + = - = - - - - 1 1 ln 2 1 ) 1 ln( 1 ln( : 2 : 2 : 2 2 n n n n ... 59045 7182818284 . 2 ) 1 1 ( lim 1 sin lim 0 = = + = e x x x x x x
· ¨ í ·ª · ¨ í ·ª α α α α α α α α α α α α α α α α α α cos 1 sin sin cos 1 cos 1 cos 1 2 cos 1 sin sin cos 1 cos 1 cos 1 2 2 cos 1 2 cos 2 cos 1 2 sin - = + = - + ± = + = - = + - ± = + ± = - ± = ctg tg x x § · ø n ·ª R C c B b A a 2 sin sin sin = = = · ¸Žj ·ª C ab b a c cos 2 2 2 2 - + = · Ø a ·ª* arcctgx arctgx x x - = - = 2 arccos 2 arcsin π π { ——Õ¬§Ç= Le ibn iz ) ( ) ( ) ( ) 2 ( ) 1 ( ) ( 0 ) ( ) ( ) ( !

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