Ejercicios Resueltos sobre Identidades Trigonometrica

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