EXERCISE - 01 CHECK YOUR GRASP

Transcription

1 SLUTIN F TRINGLE EXERISE - 0 HEK YUR GRSP 4 4R sin 4R sin 4R sin sin sin sin 4R (sin sin sin ) sin sin 6R os sin R sin sin sin R 8R 4R 5 p p p 6 p p p (s ) ( + + s) os tn os s s pplying hlf ngle fomule p p p ot ot (s) (s ) (s) (s ) (s ) (s ) (s )(s ) s s 0 e of e of x x x pplying m n theoem ( + ) ot ot 75 ot 60 ( + ) ot ( + ) ot ot ( ) 4 ot ot ( ) e() x 5 x( ) x ' E oding to question 'E, e( ) x Ros os R os os os os ( + ) os( ) os os x x ( os os ( ( + )) tn tn 6 R s 4 s ( / 4) R 4 / 4 4 R Hene, R, e in P 7 Using,, (s ) (s ) (s ) (s ( ))(s ( ))(s ( )) we get KR () hene K 64 64R () KR ()

2 0 4 s (s )(s ) s s(s ) ( (s )tn E s (s )(s ) tn (s ) s (s ) tn (s ) tn ) Using m n theoem ot ot ot (i) ot( ) ot ot (ii) dd (i) & (ii) ot ot (iii) ot ot (using (i) & (iii)) tn tn ot ot (using (i) & (iii)) tn tn w pependiul line fom joning mid point of It is medin s is isoseles 90 ot tn 9 ot tn tn 6 tn Now tn tn tn 9 EXERISE - 0 RIN TESERS 4 Hint : 8 x y p sin sin sin 6 x M H 6 x sin os os os os sin ( os sin ) os + os + os lite : sin 4R sin [ : R : 5] 0 In H p + (6 + x) (6) (i) In H p + (6 x) (0) (ii) fom (i) & (ii) (6 + x) (6 x) (6) (0) () (x) (6) (6) x 9 9 w pellelogm E E & s 6 +, 5 4 is 8 0 ight ngled (6,8,0) E e of os () 6 os 9 6 E 8 e E e e E 48 6 e E 6 e 7 0 Hint : R os os R os os 4R sin sin sin

3 I (othoente) I(inente) os 4sin sin (use ) Peimete Peimete EF R(sin sin sin ) 4 sin sin sin (sin sin sin ) 4 8( sin / )( os / ) 4( os / ) ( 4R sin R ) 5 ( ) ( ) ( ) os + os 4sin os os sin os os os ot ot ot ot ot ot ot ot ot ot ot s s s s s s s s 4 6 E F 4 H 86 {exteio ngle of H} ETH 9 {exteio ngle of TH} R R E 4 4 T H F EXERISE - 0 MISELLNEUS TYPE QUESTINS T ue/ Flse : Tue Flse, R sin < 0 is possile in otuse ngle Tue, p,, p, e in P,, e in HP, p 4 Tue, ( ) ± ± os 60 o 0 Fill in the lnk : tn K tn K tn K tn tn 6 K 6K K K sin sin : sin : sin, sin 5, sin 5 : : : 5 : 0 0

4 os , 0 k & k & () Now, (M GM) 6 () p 4 ssetion & Reson : Peimete 0 sin 5 90 / tn f tn g tn h f 90 Now tn tn f f 8fgh 4fgh Mth the olumn : () K 4 Use p, p, p () p p p pp p (HM GM) os os os + + p p p os os os R(sin sin sin ) ( R sin ) R4sin sin sin 4R 8 R R 4 /5 sin /5 Fo n sided polygon, peimete Hene sttement II is flse M HM ompehension # : n n In R Ros n, R sin n sin n n n e of ile (iumsiing polygon) e of polygon n R n R sin n 9 n e of polygon - e of ile (Insied)

5 n n R sin n R os n If n 6 then n R R If n 4 then vlue of n R R EXERISE - 04[] 4 R n sin n n n n sin os n n put n sin we gets sin os sin os sin os sin os os os (sin os ) NEPTUL SUJETIVE EXERISE LHS R( sin os os ] { sin( + + ) sin os os sin sin sin 0 sin os os sin sin sin } LHS R sin sin sin 6 / / In R R R R 4 R R R os 4 LHS s s(s ) s(s ) s(s ) s s 5 sin sin sin sin 4sin 4 sin 4( os ) 4os os sin os os ( ) 4 sin os os 8 ( ) s s s s FHE is yli qudiltel H R os R R os R R os R R os Sustituting vlues F R R(os + os + os ) H R 4 sin sin sin R + E

6 F F FI ot/ I F E Similly IFE FE Similly pplying sine ule in F ot / os / F sin EF & EF (EF) os os os os F Similly os EF nd os E (s)(s ) s(s ) (s)(s ) s s R EXERISE - 04[] RIN STRMING SUJETIVE EXERISE To pove tht e in HP sin / sin, sin / sin, sin / sin sin o sin /, sin sin /, sin sin / e in P sin Now sin / sin os 4 ot / os sin / put os sin / Now sin sin 4 (sin + os ) using (i), we get sin 5 Now pplying sine lw in we get, sin sin 45 sin we get sin / 4 ot sin 6 5 then, 4 use hlf ngle fomule to pove tems e in P Hene, so 4R sin os os (R sin )(R sin ) pplying m - n theoem we get ot ot 0 ot 45 tn + (i) 4R sin os os 4R 4 sin sin os os

7 0 sin sin 4R sin sin sin sin sin sin So, ( (os os os )) 4 sin sin sin 4 sin sin sin R /n R R ( < ) [Given] Now p sin p sin ( ) p / sin sin sin (sin ( )) / / sin sin sin sin sin [ sin( ) ] R sin /n n R sin n +/ / E pplying sine lw in E nr tn n Repling n y n we get nr sin n nr tn n sin E sin sine lw in E sin( / ) sin E divide (i) & (ii) (i) (ii) n R 4 sin n Now, nr sin / n nr tn / n + os / n nr sin / n sin sin E E E E sin os sin sin( ) sin sin p sin sin sin E E ( )

8 EXERISE - 5 To pove tht 6 s (s ) (s ) (s ) s x x y Let s y y z s z z x pplying M GM x + y xy (i) y + z yz (ii) z + x zx (iii) Multiplying (i), (ii) & (iii) (x + y) (y + z) (z + x) 8(x y z) 8 8 (s ) (s ) (s ) Hint : put I n n sin n & put n n tn n 7 pplying sine-lw in 4 sin sin 0 sin 45, ' e of e ' 4 (sin 05 sin 5 ) 4 os 60 sin ( ) 5 90? 06sin 5 sin os 06 4 s s 5 () os PREVIUS YER QUESTINS (x x ) (x ) (x ) ( x x )( x ) x 4 ( ) x ( ) x x( ) ( ) 0 (x )[( )x ( )x ( )] 0 x x x x Now x x x x ( sum of x x x x two sides is gete thn thid side) x > x ltente : (s )(s ) tn s(s ) x s x, (x ) x (x ) s,s,s x x x tn x x x x Simiplying x x sin P sin P os P ( os P) sin P sin P os P ( os P) tn s (s ) s 4 (s ) (s )