Trending ▼   ResFinder  

ISC Class XI Notes : Mathematics (Trigonometric Equations)

13 pages, 72 questions, 1 questions with responses, 1 total responses,    3    0
Prateek Gurjar
 Kabul 
+Fave Message
 Home > prateekgurjar >   F Also featured on: School Page isc11

Instantly get Model Answers to questions on this ResPaper. Try now!
NEW ResPaper Exclusive!

Formatting page ...

Handwritten notes and problems by Prof. M. L. Aggarwal Topic - Trigonometric Equations $) U))b%:##\P!\V) j "<<#V`4# j ;\ (44+ ))) 7( + A4S))'))j $PS#S#% #,)' (41) %" K)))T63) #111 !)" ^=P% ^) YW% 'j#B 6K) #11) #F) ;\#% B'''I 9U) j#B +54) .5#((3! &&4B-@--#%U)j !T@@ ( ^ ^ '$ #O@Y(Y4) (3) q4(4b4 j4b I #! !'!!@ I #P, ! #,#$ !#5SPY (n) !#C (111) ^) ^(3 (.( !#!T ` )(6 #! 9;))))) (44)) ^ (n) '$ )))p !O #\),P!#b\ 63) ^ !!(6 SSP)F% 'B "!$ '$ ^ P1+&-'''D2&PP #! #1) U))]'$ @W& ^#%^ )' #Xb5(@# 6$)) (11) !! ^ ^##O6K# #111 ^^^ #7(,4 32)),1) !O /)(7( KPC''PPP U))))]j $^j(6j#\)]%jc))(b #44) j 8&6!C Vb)))))) jj#( -> #" ^ 0? #C #-(#!O,, H j4 bY%jU`M X\''j jd)))(b p#' jU)\))Bj j#! 9 #'% E;HK! #L) (V5 j#( j)\d j &#(b](F)Jj (!' ;^] ^FP)%^ & #8\ (( ^F) -13#,,.F /(8)))h @@ (P()))$ ^^6Y) j ; F (7 ^!!#^` (3 7 $9b))((3)% !4#( ^ P #C( `B ` $\! !%(% !#!! #\4) (P( #^S ^W ;( ))) ^ (3 (11) HH(44#+4444)441111 [bmN)))P)) j jj >5) ((3 4 C&IO0P ^6K ^S) !! ))`^))jj\SP)) ;()4))))))))) #(#( U)))^))h (b( ^ 1)())\ j AU4))#\ & ')#( ))b #!#Mc)(A))j U8h j \V %'5) ,) T% _)))))U4A))))\Y))))))b4: )^^6 ))$ #Lj ))! @b & $('%())'))$! #!8#\ b)( @4)) j b))))`8#%$) j U))') jA ))hj jj j d #(1))W \bc( !L !#(!31 ``((j\\))UC4jU)))))) )#' b4E(9B7 )\4T))))(U64 (V' j =! \^ Q- !i)) !#`#P #b\ j K /#% (6 #\)?% jA))))\\)))))b( j (4b)) (3 )))b ^] U))! U j G ))b j (444311)) b ?L! 63)) (11) =( @) #S))T%MC)))Y)?) Z))))) !)' ,, & (3 ^ 4--2'''''P&--U) #5#F!7( !A4 (7 3) c_ U))]#P)) $Z%( !5 T1))!! ^ -&&?+B #\(j #, M5 )(-(M&-'' +'* @)4 ))) j % 1\( ^?(6 $Vb%j Z: () ^ jU))) #%$)(P (4) ))')')) P $T%#Y)!T* \)!`P] UU44)%#F#FM]!F! =Y)) ^ jd)))(b jjj #!TU.( &(Y $$))% ,) #O,F j #%P') ( j U)] %))#!%\ pppp U))))] j !%$ $U)% +#$$$ & K% B: Y(#D+>W%))b)EE ^ $T%^W (&( =@ ^ j *( (554)j ;U)% $))WS1 (F% j48U) $^\%#\)jIZ&j(Y #F) 4b ZY% ;^\% 3Y5) !#^?( j)))A^j R PB&PN'' \S))% ;^ ,( -9# Q ))))))( ;U')%!? ) !#P% O)) ^ )b) (W?)) #%^d))))))(@^j 1M : B%#F(#L) 9S Y ^^#C(,(111)+ j ^#F)''#?6Y (F(^ b \j FU) Pj #!MP)j (b):( +h # 5 U))]\(9b)) 3@'# H( (P !K S))B))()V*A)\)63)) U))j%$5 J j;% + ?>a%$) (& #2 ^ b^)@A?7 / ) R) ^^ !S))' ;T% 8 j Z))( #1 'W8(##! f ( = KQ.!#9b)(P(,))) (11)); \S)%) \^)* .)\WA$%jj j)bb)))))jTZ #KU)[))b@% j #!53( j Bb) ^ #4( ^ $j% " ' ;#-# &E ,0&& &E D&8 A44b))) ? ^((4A ' B))4\ $^\% M : \^))') H5WAA K-0B--5''.-P j) *( "B6# $+ ,))(,) (`V)))))_)))))))))jjj ( ^ ^ j j(B)))T)4j j $I% + #A)4)j + b^! ,) =@A j b4)))))])))dU))\ >1.)) , $)1% \4)b( K)31)% ,( j)b5))5)'( RR j% A>% j j!@W ^6$) '*! \T% )j \V))% j F^ #((# !O)))F)=U((FNZ')))L \T%3J "@'# P $q!8 #(#Y;^ )))),)),2 > 1' =TU)`))j((7) M+ `W) !jP)')j jj!K% \) $U44B% j `Y:44\)))))() jA)54)V)#P)))(# #,4)!8U) p)pp#Bjj^54) S^) (`BU) jj/j,)))))A4Y))#)^d)\ : J j j !P))) #L j O+*-(+(Qj j j ^ \U))%P PH) $!j #X))b))) #(T)U):)) j ). ^ #%$ (11) , Y(& j jjP)')'*)% ) $>))% ) 6' P j j #? 2' P!>'''#'"''&>--- + ,) KP !&9P) ( U)j ' =) ''' P >A _ 9U=4 j)b4)4&j j @4)44)j j O^)'b@I A "B6# F3%-%P 5+ )b " aY !#] ) PPB-.'G. % P j b' 6' + V:)U) $J%\1)))) M#S "L-5''# !L 6' ,)),P p \*)% WA$%OH,')?9M> , P P! ?,)^ )) @W V`h )T\)))V5c) jB)))))[j#(A%U% =OZ))((S))[)(^ ))* $T%U' \U))% j ) $34(% ^ PH)4) (WY()j)A4))))j) jjb)4 $j % D!#(b j;)% F8 #\=(4() )&I)' 3A# 'P jB))))B4j#))))) j #Xc)jU :)( 'jj ;S)% #(b H +) j jjjj!+ P# P ''.L' PP /( jjj O W\(/b)))j5j +dBX))'j j !4))\)Wb 41 ^^ #,$3 <:/ :) D A>% "(# 1 j Bb PA'''''C5- D=*D8D EM-E6@'@2K!4D ;k4 ))#S)WY% $U)% 6 )@& !2D #53)) j #0J. !& #%B (& #-( ("')'''# $D*O%J A A: $U))%b' $,+% j P >%4P Ib))))j !#(f $U)% b,) == W4$+ ))))#%% <27&' S, #X$5(:@ )* bb)j !KU)(\c);: J < . \T%,) S^11W1,PP*<'&6' b)j @b \V))% j $T% 4'& j A>% Sh %&: F#''%6L-'PP P $E'- Z#%)c)(() p j 6V)))b^*j]A j "B''# W X WW )')j %',) 7 + $T%\^ j W ' 1,(&!()% = jY) (!8@)%(44()))B )* = . \V)% \Pj 3H . WY^ "$/$#^^= #Yj61)b)!(A@jj$:)(f% ,4,() j!(jj) j j 5)' X)j, h1% b)!!& W T ;) !#`, !,+P pppp ,%#544()* ^ ,4 A : ^ @b))% ) P'4-L& UaWW%)Fj),4c!'*)% -)Q5) (W^ !O)))Z)((((OY)8)) j)bb( 5"J''# j -)j) ))')j 7 U)V) S J P IIQ jjd $,4)% P + jj\:) "B''# P 944l!) @)h b^(j9;)%(P(j $j$,,' "8&# j@YY1,D Hj% #5F,F (F( $( =% #5Q,\ >) C #]Y\ .( $HF% ^ , /- PPf ;T% j j V' j jA)) Y U))% =U 311 \D' 63) J j /N&j"[)^o!! !!#,P #\)) T% )))) eb)Kc) Y!C))G PG;F $))A)))% #,#SSQ P c] DD!%5! ;^ $j*,4,,% ;%!%^# j A: @]'' j , $j% ;T% jjj $U444\%Y,( "BH'# !'!'=P (P()$( P%#8' )@@) ) YP ,)#1$^ 3&&. KC O) ))W jU))X))V^ (b( P (Wcjjj P*2&P j6)j 3))))V $>%^ & #-)) ^=!! $U)% )\ "A# -) 7 #,))#@g) B9 T% a H''5))#!!53) j#!#(#%$) j PPB'5'' j B''I P & !, ) j^#%!#! ^ Z( ! " = WW _^jjj(( B'I"99 ^6$ ?^#! *$( , 9, ? 1.. h'~o ~ ~ t.P LU..- ~- ~ '=- - ~v 0 lj-=.. ~ er}- U ~""'c.t. ~ -I-- ~ ~"u b : o ==9 -;;. - "'---n p;;~,--u ~ ~o ~(J) ( ~ '"~ 001- (j' J'l .. . u "'-n\\/ - l. ~ c:."u to..- ts + r:;la- i -=- 0 J_ ~ 2. + J5.1:a.-~-::.0 {kL-U ~"''j ~ 0 Jv ~ Cl .,J..l~ ~~'~ e+: ~ - ~~::: (.SI =::... 0 f\ b (fL-1) ~"'X Col) ~ 1. M~ -=:, - ~'1 ~ l'l~ ~.". 1. - .. :")",(1. -=- C~" I..."X -::. -::. "t ~,,~~ I ":-\ <r 'X, 't ""-\ -t- \~ c..n ">t - ) ~') c...t?1-'X- ~ t.J?1.'X ~:x 'X ('- 'L ""-\~ , ~ - Lx _ l ~ t'~.~) ~ I \+ \Lt) N",,"L"I1. C.n'X_'}. ') ' L.n ~ - ~ I~ l-'X~?{ c:..nx-- ~ c.n'L"X 0:>?r-J) c l:9.,..."L"X -=, ~.~. -:::~ * I -::I cv x J~ x -. ~ 5- ~ " ~ I -I- )4t ~1 '+ -- . ~~ -:::. \ ~ I '-o""-J .. ...14'>'>1. J\-l c. Ln"l,. J">-f> .... - 6. r. \ - 16:>-,..J '-. ~ \+ I~ xl;. \4>~)+I '::. L. ~ \ - \c..r,"l<! c.....nx -. ko...o = ') l. _ , - {c..n ~ \ ~ .L ~ \c.-, ~J ~ .L '\.- - ..l... L / -..L. ~ c:: ~ '- '"C ""t.. + ~",-I..,.x Cv>"''ll ==> t.. ~ ..... ~ ')... ~ ~~'l1 ~ ~ I 7 ~ -+- ~1..?to ~A-:\"''L.,..- ( J!.. . .... 0 ,))..!.~">t.. -=-t /~'\... ')( ~ _ . .. _\ C-./)1 J'\.," ........I. I . -,... 0~ 11 (V }-".,. - I) ( c..u.,t'll ~I) ~ 0 D 't -I) ~ 0 -=::t ~~ ~ l ';)~\.....L~ 0 7. ~. "..- .... J.,r-~L ">L -t- S"~"'" . ")t. -~ ~'" cl- :... ~"'>L --CZUL "X-_ :1-:::.-c - ~ ~ '1, \ L..r> 1- '>t. -kJ ;:3f '1 <6 0:- - c.,., x I0 L./)L">1. - c..n"\.. '" i_ i ) \ 0 1..- -+ 1 -::.. c ~ I () 0) c.n?<.. ('l. c,o">t - 1-) !: (./) 'a -::. b.........~ '?::. j ~ -+- '7 ~ o =::.- D + L..- '='- lc.n ~ - L) 1)":::....1) /1 c...t>x--:...~ ~ '>t c...n ~ +- t. '1 c..n '),. _ <;; '1 = L L} '6-=-c..n-x x.+ --====-- d -=- ~ 4 Fo~L; ~ 4....~~~'" /.9. C ~" ;':""">\";:.. - J. (~~~\~). / ,~ ~ (!- ~'\.....">\-\ (') \ I.........~~ ~ t~/~rr] 'if ~ 1.. ~Q -1...) -:....0 \1. '\.. ::':>. ""\ ~ J I~. ~)\..;{: 4- ~ -::.1 0 'l-\. -:::. ;: __ ~ 2.' '(\ ~ -\ ~ 0'0 4-\ ~~'">I. fc.-:::.a :: '1 ./ 1 1'1 '"CJ.-. ~ -'. 1 d:: 7fr....J).fl [0/ C...r.> ':It ,e-.-A. '1J1J ~~~ Pt>~ ~ .ff" ~ 'I...::x..~ . .\- 1Jye, "-> yr~-'> ~ 1~I 4- N.. .... x '1 -:;.~'"'- x. ui - c.l~ c. \ ri, ..... 't -+ LA(X-~~ ~ <...L ~"''>I.. . {pr ~, 'YI. (l...X"'-">t . . :~ / 1. ~ -\) J.-Y ~ > (A:~~-L) >L ~">\ ~ ~ 0 p ~.),.{.. L "'9 'D-r. .w ~'" <-, ~ -x ~ r-~,-~./ L........ ~ ~ '\}C.L..LC~_ r{ 1. o.~ fi-. L~ ~ 19/~nJ i; ~l;\.0 -:n..... l ~M -- -.- ~~ I- ~ j . 'Q -:::. ~ c-...t ~ '::.. ~ ""x ~ 0 <x < L 1\ '1.~ .I.:i-..t -_. ~.-:::- ~ L.. I' .;. x , I!.' _-,_ 1.-=- ..u" . r ~~7 \-\~" \0' b. AI h-. ~v~ ~/ """1 o Cr> 7 U ~ ~~,~ ~"'" \ ,,(Y _ bV ~ IS). =- 0 l; ~ ~ .::> "\..-- ('-- ~""'+\) IL ~ Ol-=- _'.' ~ , ~ ~. ~ ~;):.. S LP L.? 'l 0 -::: 1- ~~ ') U ~ V ~ l- c.r.:.11-{9 ~"n ~ ~ t.., ~ ~ 0 I1 "'hn l;' / rrrt 'Vi"T[' ;:1, / ~) ~ ".jc..ke/> ~ ~-;:. O .. .!I <-t ($Y'" !L "\... to.. ~J - ).\ , -==- ~ r. c.p(~-x)~" ~ -x) =- t -=> :;, ~ ~ l":-" + A- "'-) - 1>.-", !-l.::..l ~ :;: L "'~, (A'c>< - >L..y) ~ e' ~'Y\.J..... (h.,-I-I) ?L - r;r-.'Y1 - '!:,DII 00-="><) ~'h0?t) A=) -ol>:;' ~" ~~ ~J..:e:", .. L, :;:-~ q (9 ~ C!:1v .!L 'Sf[ ('f .. ~" ~ ~"""LU ~ U -:::-"Y\ err !L l'LJ-\-t-\) -+ ~'\.-, ~'" L. /.w.. ~. 1>-:"" 8u+ h:'l11.~ -::. ~""'C9 ~ r' rl , - c c....Q . c..;...,~ - J~'L ILI'~ ;,...:'" S L9 Lv>:>U> ~ ~ \X. \ - - I t.:::>'-r-.... ~ I >---l>-...-I)X.) - I - -::. , 7 o IS\~ ~"''l.-?L-~''O)+ -+ ~ . N"" ~ :2.3. "h -~"'''l...x) ~"'6~ l 'h -T ..,.,(~+\)~ ~'Y\ - ')(:::t ~ @" ~'"-.,5h"\o,x) -:::t) ~ l -ec: .". '), -=7 "l;-;'-"'" ~ ~"- ~ ~'-?\ ~ ~ ,', 0. . . 'X. ;le l:: " l- ~I..."::t( ~ ~""x-=-\ ~ Co?c"::" H~~ '2...cs x) _ ~ to....TiJ ~'""- ....~ -:=... ~ '>\ 1- ) + '}.0;::. a.-...t ~ ~~'- 'LL+I 0 N.. '" ?.) -::::.D !S. "TT ~ 0 b. ~"'')(. I ~,,">t \.....1... (.4J'><.-IJ ~~~ ~ ~V<k. "\ ( \- c:..-- , o.....-l ...., ~'>I. -+ S-~""X +.J. -;::..e " -\- 0 ~ ~~:r:- '1 ) + 1 ~ c 0 ~ 'A ~ 0 0 '>t ) ~ \ >- ~~. ~"-'>t. 0- c.n-x-I) t. (2.c.n~_\)L'::::.. 0 0- 1.. _0 -I) '-~ 0 ~ 'L._ 0 ~e... ,-:::.0 ~.cd~.::)h..~~v.. 0 I G- L ,. ~ I "'lIt "1... e...c...c.--l..~,- 1- e., - c.<->">t -I ) . . +- ~ -+- 3. -::. c (C:::- en x _ \) L- ~ ~ ~ '"'J:I L- "" " -::. ":: ~ 'X 1;:: '}....en'L ')(."-, (l4 c.n1.. :>1. _ '>L ~ ( '"l'\.("'>\-\)?<'} ~ ')(-;:,. Yl....+l . .!!. -n ( '>t -f-- I) 1..../ .... 2... ~"'1.X 't c,,}>t ~"'" 'h(~+I) "V "\.. '1 -+ ~'" 1.')c -:: - "- ~(1,+I)')(-:.l4""-H).rr A", ':t + 1.. A!"" -+ ~""'1..?l-~""b'>l.) ) =-- ~~~1-t-~ ~")L} ~ -~ )..5. , ( _I ~ ~\" 'X ~ ~ lG =- _ J7: ~ J"[ c.nx. ~Ji ) \ ., l~c.nx1'::.' a..-L ~"'?l1-:::..-\ - 1- , I.e.... ~ \... ox ~ '.Co.. c--l c..n't. ~'-'X ln , E ?( L...-b...... ~"~ c...r:>?t.. ~ ~~ ) ~ o..--t J......~ ~",.t'h~ ~ (rr" X ~ C;; ?{ <: (6,. 1..nJ ~r t) ")( ~ (IT ~ Sf ) t.~. ~ ~ 1.. (L.nCP - =: ( '-.!> 'C<- >~- A) 0-~~-I) c...n cA- 'k (J) -=- ~ J- o - L~\,,~ b ' '"::.. -' /a Cn-x ~ ~ = ~(p oy ~ c.n~ ~ '" ..:..) '1~"Lx ':>.. 0 ~.P. n - : ')e, -= Gn'Lx / ..t. ~ q,"'\",,- ~ ./ C. , ~ -+ L ~ G. c",>'}o,. :::. 1- ~ = - 1. L.J) '- ")..,"- L en ">t l. c...t>L.,.,. a C-.r>x+ \ ~~. - . rr;::t 1.. _ ~ ~u../ ~r n 'h ':1 ~ .L~~i:A...x (L..~X-\) l '1:.c.:,L'>t..-+1.~X-+\)-:::" , t.? 'h.4\:. e, ~ Gr.>E '1 2- '>-l 61= 0').0- h........><.c:u....t.....!.. ~ c..n'- '""- -\- L (..n 'X+ \ ~ 1..- Coy TT CoI>L~_I-:::' 0 t 1.. ~~-;:. ~ n.:",~ . .A! "'~ Q -::.0 ~ Lr.> ">t ./ A) "';::0 c.,,!l '1-n\i 0 - A) -::.0 - (fi-+I) ) -=. J"1:--.I""'L - I) e.V - (J-2: + I J (c." 1. 4?'L~ - f.~ (J1: +1) c..r(o - + .F'f-. L) c.o c -+ .r: G/>u> ~c.r.,~':lt+ ~ ( 2.(~o ~) ~ ~-c..... ~ (4?CP + ~) - ~) , J'1- -::;> -,),;) (~ -::::?; ~ - (4->U (~Lt>-A) ~ - CSl I) ~ ~ 1.-"'7. (r.:. ~ 1.-CP -:. (.Jl X. + \ =f:. - \ er: ~ 0 . ~t...L.. / \7 ~ \~">I c.." '1=r \ (J) i- \ >,.'~ ~"')t~~ (~+ r;. ) \ ~ ~ - . + 'l.) .... '>\ L/) t o _''"/ ov ::..1. e-v- .; t.r:. ( X ~ ~ ) ~ C'">c.. ~) ~ 'X+ ~ z) \~ f) \~, -'~ \ ~(~-\- ::. - l4:>r~. .. \.t 1 ':It Eo I fh t.n rr "L~ n t 1\ c:- ~">c. lo,.. ~ru (0 ... cs ')( -:\:--c ~ -:d;> ~,,~ ?t -4 (1...'h of-,)!1. -=f- \ . L- .. ), ~ X- to laJ

Formatting page ...

Top Contributors
to this ResPaper
(answers/comments)


ResPaper Admins

(2)

ISC 11th

(1)

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

Formatting page ...

 

  Print intermediate debugging step

Show debugging info


 

Additional Info : ISC Class XI Notes : Mathematics (Trigonometric Equations)
Tags : ISC Board, Class 11th, Class 12th, NDA/NA Entrance Examination  

© 2010 - 2025 ResPaper. Terms of ServiceContact Us Advertise with us

 

prateekgurjar chat