Ejercicios+resueltos identidades+trigonometricas
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Transcript of Ejercicios+resueltos identidades+trigonometricas
tgA + 2cosA cscA = secA cscA + ctgA
(senA / cosA) + 2cosA (1/senA) = [sen2A + 2cos
2A]/(senA cosA) =
(tgA + ctgA)(cosA + senA) = cscA + secA
[(senA / cosA) + (cosA / senA)]( cosA + senA) = [(sen2A + cos
2A)/(senA cosA)](cosA + senA) =
[1/(senA cosA)](cosA + senA) = cosA / (senA cosA) + senA / (senAcosA) = 1/senA + 1/cosA = cscA + secA
tg2A – sen
2A = tg
2A sen
2A
(sen2A / cos
2A – sen
2A) = sen
2A [(1/cos
2A) – 1] = sen
2A (1 – cos
2A)/cos
2A =
sen2A sen
2A / cos
2A = sen
2A tg
2A
(secA – tgA)(cscA + 1) = ctgA [(1/cosA) – senA/cosA][1/senA + 1] = [(1 – senA)/cosA][(1 + senA)/senA] =
(1 – sen2A)/[senA cosA] = cos
2A / [senA cosA] = cosA / senA = ctgA
(1 – senA)(secA + tgA) = cosA
(1 – senA)(1/cosA + sen/cosA) = (1 – senA)[1 + senA]/cosA = (1 – sen2A)/cosA = cos
2A/cosA =
cosA senA /(1 – cosA) = cscA + ctgA
[senA (1 + cosA)] / [(1 – cosA)(1 + cosA)] = (senA + senA cosA)/(1 – cos2A) =
(senA + senA cosA)/sen2A = senA/sen
2A + senAcosA/sen
2A = (1/senA) + cosA/senA = cscA + ctgA
tgA + 2cosA cscA = secA cscA + ctgA
(senA / cosA) + 2cosA (1/senA) = [sen2A + 2cos
2A]/(senA cosA) =
[sen2A + cos
2A + cos
2A]/(senA cosA) = (1 + cos
2A)/(senA cosA) =
1/(senA cosA) + cos2A / (senA cosA) = cscA secA + ctgA
(tgA + ctgA)(cosA + senA) = cscA + secA
[(senA / cosA) + (cosA / senA)]( cosA + senA) = [(sen2A + cos
2A)/(senA cosA)](cosA + senA) =
[1/(senA cosA)](cosA + senA) = cosA / (senA cosA) + senA / (senAc
a) xCosxSenxCtg ≅ b) yTagySecySen ≅
c) xSecxSen
xTag ≅
d) xCscxCtgxSec 222 ≅ e) xxc
xCotgCosxcos
cos1≅
++
f)xCtg
xSenxCoscxSec2
2 1+≅
h) xSen
xSec
xSen
xCos
xCos
xSen =+ i) xSen
xSec
xTagxTag ≅+ 1
j) xCscxSecxCtgxTag ≅+
k) xCscxCtgxSec 22 ≅ l) ACosASenATagASec ≅− m) ( ) 122 +≅+ xCosxSenxCosxSen
ñ) xSenxSec
xTagxSen ≅+
+1
o) xCos
xCsc2
2
1
1
−≅ p) xCsc
xSen
xCos
xCos
xSen ≅++1
q) ( ) xTagxSecxCscxSen −≅− 1 r) xTagxCosxSenxSec 2222 +=≅− s) ( ) 11 22 ≅− xCtgxSec
t) ( ) 11 22 ≅− xSenxSec v) 12 222 −≅− xCosxSenxCos w) ( ) 11 22 ≅+ xSenxCtg
y) ASecATag 22 21 −≅− z) xSenxCsc
xCtgxSec ≅2
aa) xCtgxTag
xSecxCos ≅
ab) ( )( ) ATagACosATag 222 11 ≅−+ ac) 1≅−xCtg
xTag
xCos
xSec ad) yCtg
yTag
yCtg 22
2
1
1 ≅++
ae) ( ) ( ) ACscACtgACtg 222 211 ≅−++ ad) xcx 22 coscot1 ≅+ ah) ( ) ( ) xgxx 2tan1sec1sec ≅−+
ai) ( ) xxCscgxxCtg 222 sectan +≅+ aj) xxg
xsen
xgx 222
22
seccottancos −≅−
ak) xx
x
xsen
xsensec
cos
2cos2 ≅−
