Demostración de 50 identidades trigonométricas muy fáciles

1. 5e 1VU 0 H IAVI1V 0d'1oNuV
€t ?l?
8qv
eñT
TÉ
T
X
:e-
/
t"
I
X
I
¿
v
9"*t: +
="q+
9¿h
.Y
^el
+
'g t¡o
ow9
9V" rd -L3 hr 0A(rl9rü r o9.,
I
Al
I

2. X
¡n
'/tar = ttsa X *1'Xr."a :. /,-*¡t
t+ x.F
I + xr-t
X,-Yt - 1 = XrV
xw
W: Yf
= XSsz
= X retg
f.qr
ñ =xj
: 3-LN3 r ?r) 7te
yz*t9 -l: Xrvrq
Xtv | = Xzh
Xrtel - | = XrW
/ = Xr* + /rY
: sf ?l? gev _Ll ¿
*w-- = X á¡0{
,+
/ng
T: xtq
/cn,é--- = /4I
r?4V6.,JNeGI
>(vg
--É I
/ t-r¡
I
Xqt+
I
: ) )9'¡
= >w
=yWT
9v;denNu

3. t
a€
>ryJ
: ?r
>a ?"9a
*a4
= P.W
- o Cl)3¡
-
Pv9
.t
2,o a4
'Y -
v.wi T +
*z@ 4't =
7zryt
?wa-.--á
7
:w7
?"3
T,+ *fr
-""52 - | Y
?+ -.F
*W
,'
= VQS€
>j
-éé
v
=fr
>ozr9
h*- : >a 60
v
a?j
i, >o W9
:5V5Alltlvl
v 2s?
*
v
m%¡
a to .> ++?5 = -P AY)
f
-r¡ -...,.o{ )o 19e = )o w
{
(-*+r)(**-T):Fzw T
(* {,? + T) ( .,L=J - T) = ?zc.€uJ - "l
*¿'(t-?)(l+3) =.ol -,v
>*{ 1q,@'7y W1*asvt Y 1* J_
€ -o%l
+
:3.L. lvSl?oc"?36
* t&a
*24
:91?ldogvJ' ¿
.l
5?7 VJlvShtV qArnJ 93(rflqrJ A.'Jqr

4. ú
Xn4
Xav-a J- X wt
Xrwt X z4
Xtfr X ztrJ
X zwl
= T + xzf
tu."!-
r ¡a¡
x
/.4
X zel
I
LTx
X ntrl
+
Xo4
+ X.
X"4
X¡*a +
Xrwz +
Xvn-r
X -q9
Xt%
+ yfft
* Xfi "z
xr
xFt '/.--'T'= xurÁóiXíH6--
f./
'xi
, N??vVJe^Y,t9&
: Xrm + X"t++
xy
xr
x r.xi
x#
T + X"fl -'€
=ett^-.r eT+t'n-+u T ¿ VtoN +
Xrw
-_-
T
¿@
x aw?
w -rb
-Y
:ígJht-eto?/g 5?dV{tlNl(t 9V7 ¿t v¿l l90w1a

5. -9
t--1
lX.-gl =
xrw
I
X, urt
X¡n * X r4
Y- -F
Xrffi
't
X ^4tft
xw9
Xqs
I
/rw
-é-#
v
X z'ry7
X ot-rl b
Xzfr
Y rwt.é
Í xnw
Xz(a
-r-
@-
=' Xzqt
+
-.4I
x?r2 -ry= xo6+7u6't
;¡e€; 'X.'tÉ: Xz@+Xt!,ttr-
xesc.x4 € xtz<'a * x.wt -'j,
Y-..r,-1-?
x uoe
É
--
2
X*3
XW = X+{9 'X'v+Úg
W r¡,o.{ : y ?ú Xe '" h
;(cs?. X-e + Xz'41
x-oo = x"sa'X*re +x;!..|oÍ.¿'l
-==-^ xrlgz
'r =, Xrna+ XLwg = xr* +
---
?
f-
X a¡a
2-¿ =a- naí2
X .uoe +
X *se
,

6. ,)
lr,*l=
lrq
Í
Xn'm
X¿4 + X aryt
Xoq
--xrq
X te?
-L
-É' Xtql
1+x-af=
ry_x3 + x',i:
X3L.xj+ x-ry =
I
X z?xg :
l2l
x*,
x?ia
/?"r
/ú5
X*xt -t 1<
I
'XLe-a a
X >tl
XrQ+xr4
Xnw Xr'l5
-
Xawl xy
/o4 "ü
X'-g
/ 1/F"A1
x# t'g
1 tfa
I
X r,ú
T+
X¿?9?
xr'x. T!" + x:4
xr .xj + x.Í "Q)
/6*;x$-tX.@ + xawv
' Xtn
X {v9
?'>(ooe, +
Y .?sc -l+

7. +
y ye'7
/ csvS
fi;*n + XoW
xq4%__
=
XzW
Xtn
X *vsg
ry/VJ
tl
ñ.'-T"YtI
x<Ft
+
Xcn
Xts¡
X*.tg
v
+ xqJ'x
'!fuL
+ t csra X"}[ -'Éi
-| Xr%
+ Xo4 "zl
f,
--t**--*el
lo,*l =
1
X,W
*T=
X-.4:
1
Yrcrc
Wxo*ú
>(rtn Yrcee r +
-
é
X.É2 X¿%
X r,ca
xr@
yz,cm
O+
| , /rwvXr@ =
-'il

8. g
x4
Xeyo
Xwg
I
: tsc 'X'el.)
/un
: __
xwt
Xry9
X6a
I
Xy = Xr¡" -Xr'l) -'?l
Xws
ff--,I
X"s, 'Ncn
I
l,tsc 'X+¡y)
-.sl
Xrc-r2
-
X ¿"qj
"Xr"4
x ."*4 2
X¿w + Xr% =
4- +xz.% =Xr@ t¿qt/
>c3
<.
X"fr
Y-wI
x¿4
+ Xr%* X"%
+ X"*rt "hl

9. b
-.-')X"tsc =l
Xo4
c
I
XoW
Xrw + X.wa
xo4+ffi=
X.j
Xzw
X..4
txwt a
Ytm
xwv ,
I
Y.csc
Xv"Tn
€-é'-'
x -f.,
Xu-t
a ' Nwutb
f,*l
= -t +
--
-'8i
?
XY¡s 'XY@
I
Y:a9'Xt^4 '¿t
xr3

10. Xz4{"W
-
-
-I
Xa*tj
-
*nV
T,
/q
--_r-_
xeJ
I
xls) 'Xc¡n
*,-4
-+-*-Yr,e¡e
X-*
Xrffi
XoV#
X¿rrr-
x#A-
' yr{rt
Xrcsa
/ .,'nfP
+
t
X* - Xrst
I
/*t ' X1/v)
+ x"r
+ X" S" 'a('
Ytn"*
fy--'scl = , = Xrcct t"
X.W
X.w
X z-'^T)
r% e
"--
Y to?/rz
*i*wq
.---:F'
X*'@
Xoú4,--
X.@
++
x4-*=4"x-''-la-
l
+
X,nl_T XY'Y,@I
+
*.4
-.--
X.@
+ lrf,
.x,e'l
X.caczffi + x"f. 'bl

11. /zW
yJez X,W
I
/rw
ffi +
T
X.vq
r =
*Xw¿ =z+
X*sQ =
>(*s
-
,(q,
,-
Xv.ag
.yv+*
T+
Xz@t
r,_
Yz4
X.@
X¿e
I
-L:t yrwr9
X"crt
+-Xz'4 I
Xtsc,X4
+ X, t^+lef
Xrq+Xrwr+Xryr-
X.tee + Yzw + x.l-
XcSc 'XvO
'zz
X,T + X,y 't¿

12. 7l
{rol
lz4
/, *t
-é
- /t%
x+*,
Xl"f,
/wl Xtst
>,X'"z'9=6xw
X.*rg
TF - x¡sz
tr ''xrv"t9
-- XTra 'Y --rl 'hz
x sJ t4
é =-€
x tq9 Xwg
X vrú
xvñ
X'*tg
I
:. F..-.----..-
7(tr.,,
s Xcm
h-ÉÉ.
Y +ts
.r--
'1"

13. et
/.@
h-.-
Xz@
X-Q +'x ?,W
ry- = x,ur *
/zh
.'
/.4-'XrW
#lx,@
: Yzgoa ,d
floY<rr-far- t"tl
X"q
I
V' Xte
7qo
*n[+l ='f,*
/"q
-.-:.I
{ra
/n@
yr,.rt + X.4
Xr%
xr9
I
/rv)
/rq
f
v
x4
*rr+E
-lt ' Xt'ar9
I
Xts?'X4
X.@
I e---
-r X z'4
/rW' a1n
XE *zñ
-=
lr
Xr@
I
V.P_
I
xnf'
t
+
+x,4 's3

14. Xrt*o'X-za =
ht
,WW Y brü "r--ng,nU ,* A1 O
X.Q'XW
-----. l
xrw'I"@
I
X"q
'TXtw
I
X --5'
+
+
Xtq Yr4:.
l
Xr.4 : Xrtg" Xt+'*' " gz
{rt
t :' Xrccr +
X.cs.-É
t 'lZ
*-4:
>(rc¡p
,
/'*t
x4
/"-S
I
/qt /r@ + lrw
Xr-ú
/rw xrh /:.wl 'X-*t
T
Xl4'Xr"a
X"-W
I
X'4
+ -€I
7,oW'Xn'n
: x?n+xf
X.s'X:-vaa.
/1¿-r'./**e + 'j?

15. =-
.9l
xwt
-
xt-/)
xqs
-T'}/cr| = Xc m'X,t)
X f =. Xoy¡.X cñ ,Ze
X ('.'J
é
x4
x<?
. --.-
'l
/tm lcsc' Xt-n
I
XtU 't;t¡
-t2
ñ
>-ó.xch:4 +W;Ya?s'T=
Xcn.x:lsc-Xttr+ XW.X)rp'/,>zi = (Xr^ + X*"v) *t gc 'y+te
(Xr,.r-t + Y*rrl s) X)sc'X>tg =- I csc + yzrg 'bc
mx4
/tn
. É t
I
XY 1=.

16. qt
+
.!:4
*t@
/n4
-Xzq
x*4
Xz@
x 2J-
fl+
l
Y3.xYl'
xr'x4
X+3'Y.'-.l
+ lrf
+ j, F" ')'e
I
Xr+?j
-
=X%
Xwr
-
t
Xw'.t
I
Xt?t 'Xn*tA
l
XtS ' Xaq
/.%
I
X-4
d;'ot 4 X--4
y'--*
/r4
* x.f
/rcse :
vr
/ ve2
x4r-.
I
/y ee

17. ¿l
X.-4 Z
{r9
.L J
v
Xat-o2 Xl,qS - 1
--
=
-
6V
.X^üg - T Xr¡,rg t 1
+
v
yvqt - "t
v
ywo+TXr>ta z :
>124
Xw¡t C t
t Xz?j
t 'xwt? + t :
s{rt y WA *Xz.?"+Xt*tí :
lzt*t + lvv2yvet? + X.-y =-( X*z+ Xr_O
X*¡ + I --
.(*w? + Y*)
+
x',,aÉ ¿
't€
-.2€
xr@lun--
y, t-n /¿4 I
Y.* Xztcl
xrry - -¡- = X_u'*l- Xr+a1r+
X-i, - /24 = {.-.* . * YrY '-g g

18. 8l
xr,%
--r--
X¿4
X,Q
/aun - |
".too_ _yl¿q I
I - X¿>79
(,n xñXr-Y-')
l- x?ry
y?4, = 7 '5e
Y >Se
-/ -l é- >1tqt *r:
/qsa, Xvat + ,
xzq
,l.na * T
X¿%-t
/ zsc --r
Tr
X"3- =' *"*?
= X"*l+
= /"*T
X,
X" *?.
X.wlf
t+xat
Xz
I + X>zs
E -t
e?ñ)
I cJ.>J ,99

19. (x ,-" * ,) X v'd
X¿te, - I
*ws
=W-xrw '
><qj
T
>A!,t9
*-n",
Xtr'" - |
x4
*tao --¡¡ I .zh
X+:, + Y "la+
^4
/ro, + t
ffiz(",-")
X"* + /o% =
(o4 + (;'-"t)(x wt) =
X twt r X..*rc yd
w,T=
Xt+rg -Xtm
ffi xh-¡-- ,
X'+3 Xr¿j
Ú.-:l
-
/,t.Jv2 ){.qg-
Xq
X >+ía
x"+9
-th
Xl-*7
.'-+
ltn
Xv¿E
I
-i¡É-
xv.?'g
¡1 :af
yun
y1d*
--'F
X c-c-l
x "
5?
yw9
/,cr¡
---xw
+
+T 'oh

20. = Xf *¡csa:
f n*o
--
tt,re
-'--t
Y[,oc * X.g,
Y¿loa - X.¡ga i
Xf tx>sz
x% xY -lrn+X)s) :-.sh
,t
/ n'+1
X, ttu?
x^n +x%g.T
-w
X,Q
-
XtV- |
Xtwl
-é
-
Itnj
)6@2
I
w: x"4+ /,?+"
av'a{ + X}19
:r
(uZ- v'+ -
-'
-/-
X""t ^ X+tg
X.41- Xrat
X w1 + t(,za ---'. - hh
>(*rs -l I
>(q
(x-'s+ t)xw
(x"+ +t)>á
xr*
l-q + I
X''v, * l
lt-*z
--
Xv+tt - I
I )+ra I
-l
(** - t/
l*t> + I /'.1-?J
X"qr + X>4
:r
XzY-t
xq lwE t €h

21. /u2 + I
B
(
llt
Yt¡a
r *--- E
t
(x .t¿a - l)' x v'a
-* tJm - I -
X ¿r{'rf . ){Jtry
Y¿s?'l
X.w'/Á Y ts,a
=
Xew "/+v. x I'F?
xqs-F"r ry
/ r'ol * Xrn¿9 + />s. =
Y r?e
i(r"5=T=I -' + h
YE-}. ¡-.l-
I
/,xs-+
X''rj
(x.^"t - )>(%
/r.4'- l
¡1w> - I lyrg.I."167*4-
XtQ
'lr,6
, X.r6
rÉ €
-i--
dvta I
E xtcQ
| ^X csc
-
"x"r
s'
#
>(
-s
/',ra* I
X¿44
xzn
l' Xtsa

22. ¿e
Xwa.Xvüg
f4,r9i-h¡rr¡
,'
X )iz yc 9o
/te?=
Y+:" + X*l
>( >g> -.09
W'.W
X tl'¡. X v.'¡'g
ffi X )Cz
Y-a Xt*l
-
X re" Xg
IAA
-,
)
'btt
X t.lco. Xwtt f¡v.t X toz.'lll¡:.--
)1 t-*2 Nw
Xloo XqY
:xr+x"aXoW
W ..o-¡ * Vfto,l .atl.