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inverse and hyperbolic

inverse and hyperbolic - Inverse Trigonometric...

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Inverse Trigonometric Function/Hyperbolic Function Identities for Inverse Trigonometric Function: 1 1 1 1 1 1 1 1 1 1 2 2 cos cos ( ) sin cos / 2 sec cos (1/ ) csc sin (1/ ) cot / 2 tan 1 cos2 sin 2 1 cos2 cos 2 x x x x x x x x x x x x x x π π π - - - - - - - - - - + - = + = = = = - - = + = Identities for Hyperbolic Function: 2 2 2 2 2 2 2 2 2 2 sinh 2 2sinh cosh cosh 2 cosh sinh cosh 2 1 cosh 2 cosh 2 1 sinh 2 cosh sinh 1 tanh 1 sec coth 1 csc x x x x x x x x x x x x x h x x h x = = + + = - = - = = - = + Derivatives of the Inverse Trigonometric Function: 1 2 1 2 1 2 1 2 1 2 1 2 (sin ) / , 1 1 (cos ) / , 1 1 (tan ) / 1 (cot ) / 1 (sec ) / , 1 1 (csc ) / , 1 1 d u du dx u dx u d u du dx u dx u d u du dx dx u d u du dx dx u d u du dx u dx u u d u du dx u dx u u - - - - - - = < - = - < - = + = - + = - = - - Derivatives of the Inverse Hyperbolic Function: 1 2 1 2 1 2 1 2 1 2 1 2 (sinh ) / 1 (cosh ) / , 1 1 (tanh ) / , 1 1 (coth ) / , 1 1 (sec ) / , 0 1 1 (csc ) / , 0 1 d u du dx dx u d u du dx u dx u d u du dx u dx u d u du dx u dx u d h u du dx u dx u u d h u du dx u dx u u - - - - - - = + = - = < - = - = - < < - = - + Integration Formulas for Inverse Trig Functions: 1 2 2 2 2 1 2 2 1 2 2 2 2 sin , ( ) 1 tan ,( ) 1 sec ,( ) du u C valid for u a a a u du u
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