tgA + 2cosA cscA = secA cscA + ctgA 2 2 (senA / cosA) + 2cosA (1/senA) = [sen A + 2cos A]/(senA cosA) = (tgA + ctgA)(cosA + senA) = cscA + secA 2 2 [(senA / cosA) + (cosA / senA)]( cosA + senA) = [(sen A + cos A)/(senA cosA)](cosA + senA) = [1/(senA cosA)](cosA + senA) = cosA / (senA cosA) + senA / (senAcosA) = 1/senA + 1/cosA = cscA + secA 2 2 2 2 tg A – sen A = tg A sen A 2 2 2 2 2 2 2 2 (sen A / cos A – sen A) = sen A [(1/cos A) – 1] = sen A (1 – cos A)/cos A = 2 2 2 2 2 sen A sen A / cos A = sen A tg A (secA – tgA)(cscA + 1) = ctgA [(1/cosA) – senA/cosA][1/senA + 1] = [(1 – senA)/cosA][(1 + senA)/senA] = 2 2 (1 – sen A)/[senA cosA] = cos A / [senA cosA] = cosA / senA = ctgA (1 – senA)(secA + tgA) = cosA 2 2 (1 – senA)(1/cosA + sen/cosA) = (1 – senA)[1 + senA]/cosA = (1 – sen A)/cosA = cos A/cosA = cosA senA /(1 – cosA) = cscA + ctgA 2 [senA (1 + cosA)] / [(1 – cosA)(1 + cosA)] = (senA + senA cosA)/(1 – cos A) = 2 2 2 (senA + senA cosA)/sen A = senA/sen A + senAcosA/sen A = (1/senA) + cosA/senA = cscA + ctgA tgA + 2cosA cscA = secA cscA + ctgA 2 2 (senA / cosA) + 2cosA (1/senA) = [sen A + 2cos A]/(senA cosA) = 2 2 2 2 [sen A + cos A + cos A]/(senA cosA) = (1 + cos A)/(senA cosA) = 2 1/(senA cosA) + cos A / (senA cosA) = cscA secA + ctgA (tgA + ctgA)(cosA + senA) = cscA + secA 2 2 [(senA / cosA) + (cosA / senA)]( cosA + senA) = [(sen A + cos A)/(senA cosA)](cosA + senA) = [1/(senA cosA)](cosA + senA) = cosA / (senA cosA) + senA / (senAc a) Ctg x Sen x ≅ Cos x d) Sec 2 x Ctg 2x ≅ Csc 2 x Sen x Cos x Sec x + = Cos x Sen x Sen x k) 2 Sec x Ctg x ≅ 2Csc x h) ñ) Sen x + Tag x ≅ Sen x 1 + Sec x b) Sen y Sec y ≅ Tag y Cosx + Cotg x ≅ cos x 1 + cos c x 1 Sec x i) Tag x + ≅ Tag x Sen x l) Sec A − Tag A Sen A ≅ Cos A e) o) Csc 2 x ≅ Tag x ≅ Sec x Sen x c) 1 1 − Cos 2 x f) Sec 2 x ≅ Cosc x Sen x + j) Tag x + Ctg x ≅ Sec x Csc x m) (Sen x + Cos x )2 ≅ 2Sen x Cos x + 1 p) Sen x Cos x + ≅ Csc x 1 + Cos x Sen x ( ) q) Sen x (Csc x − Sec x ) ≅ 1 − Tag x r) Sec 2 x − Sen 2 x =≅ Cos 2 x + Tag 2x s) Sec 2 x − 1 Ctg 2 x ≅ 1 t) Sec x 1 − Sen x ≅ 1 v) Cos x − Sen x ≅ 2Cos x − 1 Sec x Ctg x z) ≅ Sen x Csc 2 x w) 1 + Ctg x Sen 2 x ≅ 1 Cos x Sec x aa) ≅ Ctg x Tag x 2 ( 2 ) 2 y) 1 − Tag A ≅ 2 − Sec A 2 2 2 2 1 Ctg 2 x ( 2 ) ( )( ) ab) 1 + Tag 2 A 1 − Cos 2 A ≅ Tag 2 A ac) ae) (Ctg A + 1) + (Ctg A − 1) ≅ 2 Csc2 A ad) 1 + cot 2 x ≅ cos c 2 x 2 2 ai) (Ctg x + tan gx ) ≅ Csc 2 x + sec 2 x 2 aj) Sec x Tag x − ≅1 Cos x Ctg x cos 2 x − tan g 2 x ≅ cot g 2 x − sec 2 x 2 sen x ad) 1 + Ctg 2 y ≅ Ctg 2 y 1 + Tag 2 y ah) (sec x + 1) (sec x − 1) ≅ tan g 2 x ak) sen 2 x cos 2 x − ≅ sec x sen x cos x