Fundamentals of Mathematics: Trigonometry (for JEE Main and Advanced)

521 Pages·2015·20.15 MB·English

by  Sanjay Mishra

(0

Sanjay Hishra

PEARSON
Fundamentals of Mathematics

Trigonometry

Sanjay Mishra
B.Tech ttt)

PEARSON
Conc 2s Bean Tain Edn ioe Po C8

‘el ty Rew tn Eee Sano 2 La, CD TSACTRLSPTCESUS, mele
2a Lani ce, 4 fests af aon Resa: Sen ia

Sorat tse ok me Meal on epmdinndin oe mm hero he Be

‘TheDrake ei pi ve. Th eras
neha iemareaf wad ots Baska Une

Nyda 48 hh Ra le a Sed i 250, Uc ae
iil. Mol Gano He Sale nF 1 lsh 22 2

sb Tesoea Chi, 0 113 Tea Mad ob

Fe Me, O39,
Contents

tdsenenes vil

Invsstson 11
PanieCoveers 11
(Qundrets andes Sgn Canecacons Le

Sige Comer uma gle Tn
Posodiiy and Ponasie Fanetons Ls

+ Peopemes of matey

Liam Fine 8

rupees af tvrm ttn

onus Fraction 122

‘rigonerrss isa Phew Popes 1
+ Senstt
Trigorsmotic Ldsncties 1.16
+ Syhasanan imines

‘niga ain of Some Sts Ales UT

= Trigunoneivic Raia of 58° «Picea: Raia of ont 0
2 Tigunmetvic Ratios 0 ond 90°» Sa cand Paces = Cin and Ses
D Tavrand Cats

‘rigonnnetc Retin for Alig gles 1.22
Uioucneine Hlnasol fe Chan Pena of 21.26

Inter-soncesion of Tgonemse Raiot 1
Foran” rgpmmet Kaos Girnsanmal gl

= intrnptppicesen of Sahai ofen ingle « Sam san Oerena of
Tange aed Cotangents Cams onal hore ts Sed

CConesston Fomnues Su ints Prods:t 1419,
Thigonensi Hain actury nf mason Vins Anghss 1 al

Conditional deotines 44
Appeation of Togonow:cry tor Eurunaiog Viibles 1.16
Ssivuae a Vinay Valse TigumarvrioSrione 188
Arphcalin of Teosy 0° Equi 1.53

+ leptoononeaaned 39 Cwatrane signoron

Asplvalion Os ng Traoumalior Payton 183

Prowng ignsometio Isgualiss 35

sensor > Panerai Maton an lvguatte ct

Apphesatons + Dowson

Srorttion of Seis Crane ew Cava Ags Faas
Sino gle Fe

ing S%
Come of Angle Forming ar AP 5%

sgpheuiau Cages Serbecs kr Su Lngeane.as Secs 6
erles imi ring Nhu of Lief The frgls orang GP 6
‘Mutiptecholee Questions

DOhjsative Sev Faw pes

Subjetive Sales Forages

Tov Fsesast

at oa Soitions

Crapter 2 Trhgnanetrie Equations

TWossation 21
Triganmer se pais 21

+ Sohn oftrigononeire Soustont © Fartoukn Staton © Frnipat
Kaltnors anna! Seton Tevmnd Solon of Eqaotre Selb
Genera xiao af Eyton Lan

Teundert yuebons 2.15

Anypectan Pointe Ramsnber 2.13

= Cason: § » inti: 2 Costin 8 {Doman a

‘guatoe) «Gaston: 4 oot Loe tan aston
2 Canton § eines Rts)

Sununu Penansss Ronan Toga’ Rot 2°F
‘rian pais Sone Swe Tr 938

# Myvarion of rm. Coax = bSone of © Rgaron of he Fora: 3 Si
BE pSim ence a, ee Cate wos aCe thao TiSgonomatic

Pancinn fhe Porn. BS ks, Cone Tam wa Cats) = + Epnstan of fe
Bor Te (Siny ene, Siny Caray = tgwaton fenbang Higher 00
Power Sing sna nc

Solving Samullvoose Equaaons 22

© Secstioon ith Onl Oee Tari + Fipwaions with Toor Kae Uae
Vali ene Tiseon Pater Vals of Sn rand Coes 238

+ Iipet Tapsaomene Squaions Hvala Sash Viole

1 ype it Fronts Mpuanons tang tor: Than Ons varales

163
Les
Lee
fe
Ls
Le

2-208
Chapter 3

Uesosceseuel Lsuatens 2.35
‘Scasucal Solutions sf Pquations 278

Solving “vecustnes 2

1 Rove af Sow: trenton Irigomomtas Lohes
‘Mulepe-chotee Questia
Subyeeure Solsed enum

este Sol Fg es
omc neat
Jove Kons

Sins antSohs

Properties iad Slatin of Triangle
Twain 27

Pupation fT arale cas
relutioFTrnghses 1

Sine Fovenche 4

1 Aepicoton 2f Sta Hoewala
Cones Forsia 3.4

sofas Freie

= Aoi
Purvi oma 4

apie aha Tango ue 1

ToT iad Fe Sine, Caine ae Tenge ofthe MeIPargles wTaamotile Ses 41
Areas Irie tae 312

ve Thana (CocangsilTheoneny 16

Selatan of Tile 421
Gur iilet Herpheard angh uf Meise 428

© Ley of ediaas «The Aaptes thr te edn Mees with Sider
Gucumcesle ond Cesumente of uirgle 329

ancunde of Inangls 329

Heonbod Chloe 330

‘etheoea se Peel angle and ts ropes 3.35

CCueametsloof Pole Tenge this Pot Cinde) 3.46

+ Parris Wee Poiat ie

Thee sort Theale 332

1s Geno Lasso ac imi ths Crear Oilhazatis 38

The Las gh ul hele Bate sedle Angle Tha he Risen Ms wid the Wes 3.
The Fever wl Arch of a Tega Pola of wide Teas v ails 162

1 Penn An Regul Polyget soos Liana Abo ls

‘The Ril ofthe al and Cisne bing Giclesa’a Regula Polegn 3.42

gaan
Chapter 4

‘Mulipk-<toice Questions
COjoative Sn'ved Fates
Sal etve Solved Frans,
oma eee

Anas kere

ine vntStnrone

averse Teigoaometsc Functions
Aniecestion 4.1

vere Yincuso 41

Ansere Ingoowneter Lien 42

CGupasel eve Grcie Fenokoas cl Iba Demand Range 42
‘Compontinn a TopunansieFsndcosapd Tis “ovens mc

sere Cuter Harlot Ther Comespoaing Ingvesnetee
Ferien in Pinisal naa 1:8

Ties Cina Faeting of Thee Consapunrg Tigra
FercinoyiaCoxplte Doane 412

verve Ingoooctln Lansisas of Negev pale 26
vere nguoomiet Lt o Recon apoly 428

Inter enveraonef merce Ingensmetns Lachons 29

“Live imperial Heou:e: af laverw tagrnemete Functoos 4.37
Musplesu° ata Irysouernc Fuacbous 4.39

Seriand Sucbrerveo.lavere Ingoneraein Funsiuus 4.35
“Muttiplestolce Questions

Cctv vel Kegs

Setyeuve Selves Ssamsles

Toro Feast

ingen kage

44-3

a0
46
rl
4st
48
ast
Preface

The vind Trigenonely’ eG
‘Gow, wich pens x “Ange. Th suack of mclaeraes a9 cere ot tbe Inc soc for u umber of
oon iy Tada Soke Ae Bled {36 evtacy AD}. Vala (6 cea ACT. Bla Cap retary
‘Ay. unkura 112 orale AD, uo ier t we pave va toe Wes, een Lae Abs, aller Lik oeary AD. at
fecha Thaw inthe inn esha Tegument oe omnes mbsf ge ngs ae he
“Vita th estury ADY cna Looms ale (188 enty AD),

Ire sons days, Loa suyli”Figomenehy Hy cme mal ata of maremring safe armies
fg [eveloze4astor¢ phob ef hs seo but sr op. wheal ted to uode-mas th good and o-igaat ingououst
rieTenaion: alte wspaticg, Faas sleanhofautarliy seca ead Salengng rl
Jone ixough vrevp.ual appr to -eumis seaemaing a suk,

Tw my senaycirg dot ny High sla Saya, ae TTT TRE amit “at aa ake of Vata
pas lutsen yous bays tho vod of x commprtensive xt book en Tegono-moky bal els muh dhe arbor malice
meaty

‘ns book as teen well wth be ob ote of sevuding text bock se usin sere ek, corns pte

oe | Rtv) race anu of brake wa va er the Cheek sal

Ten sulviag "fe thine trl Gt the wala Soper, prwulloge tale Stunt of Shean XT axe XM.
be claeet he equremeri of ware evel ules ose pepenag fr vanou enlace ese clsas HL LIL
AINE HIT a nlc sate eneerea ng ena ecarPutions Hs Ieok,sigomameny, sess dg Tigh
ante opie: Tngotaricts Fanta. -tigeaemeiqoations ct dts, nwo: Trigesemmesio uation ad Poser
Fo ral Sh ewset Franch: Ths vllragl cnt bl el el tcknte sl shat use wena
tho captors and subtopics of es teem ach chaps edad ie sever topics each top opts teary abd
oe sive sulin wih licen vad src tot ve pens Sak vasevelye aha

ay of Lae eobcepa seul. Tiss olor bya edu exer af bole cbjvtive ad subjective ype proslemia, se Use
reapivoments Alike clothe tayo ech clap. a wgestof on val scat oh osisaive ard alizclivetype
agen Thy wil avo) upplisaoo of ul IhecarsupisJoumt wo thochepler so tbl 2udcscan Jessop ros overs
hap: Chetulvileseieryivanst aod ones scrub of enki ccs > oom iho al als
met op ons, compreheuser pages, coho auacarag robles, cumercalinlege: ype cuesisas Keele tbe
Sudevarudoacthacaugh isi he idieu qi snd to ie “ck level of ualtanlirg of Eris Fo in
tay st bole mal he gee Welpol ava wll proven. of wel, ide poles ged pew eu HEN. Be.
fe aes ae gen a talent
A suggests tor mpsovatcen ats welcome and sh. se gusty ckamledgod.
h

Acknowledgements UZ

Tan zlle tal te Peasun“sactoe faking ih ia aa ‘x ying mee Ir ameppolay arse
yearumg.ny yearsolexpeneece tr evbine aE i mpwledgem.0 a prmalcompcebenave es. 2k: uiowentalt
Ui Mohewaticy- Prgomoarrs. Vor like Crk sl re Pn ncn Thc a ait ar a

vad aeetce aa wae zeny apo oko k, <a plese Uo anand spec vcknoreegeraets Wo al 23
ile During ae int-astions ith ay amon. Tavs got mh of he ins ation fo ing his oan. The
‘hat Pe iteracieg we tare. have Ime eh more than I sd have ever ght her, Hm te Rank ey passe
wal lly fey wobe, firth tence aed woe aging thin a al hatin Hh wal bls ane
tne Sr such cause} end ay oscil has co Heksah Cpt disc Juda. Sant Sinha and of (ca wombers
f MPT a, Sa sos TL fy Ui ans all ln i oping Ek

—Saniay Dihes
Trigonometric
Ratios and Identities

\ouneren

Hfinrropucrion

Tw provious clases, yon mat Faso teat te pcheaonas
onto 1 Gooetetry “bat aig ang wage tb> 2m
tape of vase wen alate ac inca to
tho sque of he ages. i Cepstocns Ts Loan
swat sare ily wad fiw apes savin pplication seg
Tesiag deo [se soaudanes of he ld ot igh ager 0
AKeding ig sagulr une ngs wae

Te chose teoren:9 cue Fer gh mg.ed mag
‘oer th el su thesis, Ssh 1 aval ehe
‘comp reed ea

The wal Thigenerens
of mingles Ig w sex ceaved fom Gein, tees
‘word. mois an ang Ths franck of thera: 28 Ws
‘wits ot Indao sol occ sumer ot sessties by “us
sebolane Hie Avyallica (2h Cat” AD3. Yasin
‘6 Cox. ALD, Secooegupla (7. Con, ADE aod Washers
{36 Ca AT) bat La i ae ho He a th
(ho seubs. le ie th eevlesy moder tgonomcuy 08%.
Sans tf ths wovks wf Taro we navae re
‘ets (Kita Gen AD) ad Euler Uh Cop.) and easy
seh cnn Lats

‘tone is > base vompanent; 3 sues wo bree
engl. outakoa rangle até inoieate ioe ibaa
yer vel ve lo mize eee come aber xe or vee
glean thar the ce sds and anges tle
lepsudent or tte 1s exueclaioustip boa tat, 1a
thie shopie, xe al earns tere ndon Sere ul
‘ee eladousbpe ace aba sue xd bere ye call ae
Irignmnresi ies Seale Thee eos
lee lee their vanes applicatooy io sais stvams of
fucaati e ta

1e coments ss chaper form element tool ot
s-sntfie woke Be soul nt ory hve shape

stars the: meanuemont

a i eget te so a oe Tae Bae
ou. ene re al be ei Wee
jeg af david. Te this soso, ell aap Izam hase t0
appl howe :alhecica nso galore
shthenais at other bane of seence,

iibisic concerts

Sapo «cet is looking a het te FE fone
271k tangs vento gined ts to made. as seven In
Tae Fre Hen Coat the bh ote if

Sock, without ceoaly messring

nll alten Le Ihe ne ven ve, the dice
the eight ean be Fauhd by using seme meberatical
sbuie which center ler w beak «maka
calla tignometn.

Tre wont Trpenamiteyiediivad unbeotneas wale
HF “eign sod
3) iron The sl ign ses Hi te

‘wen eo eI a pease s0:0 L-popORKY
ve once of ing nn This thin