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1 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge Generl Mthemtis For CU & GCE Mtriultion Chiu Ming Pulishing Co Lt Eerise 8 (Pge 5 55 Q Q6) Prove tht os os os ( ) Solve the eqution 4 Solve the eqution 5 4 Prove tht 5 Prove tht 6 Evlute the eterminnt 7 Evlute 8 Ftorise 9 Show tht Ftorise Ftorise Prove tht ( )( )( )
2 Show tht the vlue of the eterminnt Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 4 If C 8, fin the vlue of the eterminnt 5 Show tht 6 Prove tht os os os os os os os os( ) ( ) os os os( ) ( ) os os ( α) ( α) ( β) ( β) ( γ) ( γ) os os os os is inepenent of ( ) os( C) os( C ) ( ) os( C) os( C ) ( ) os( C) os( C ) os os Thir Eition vne Level Pure Mthemtis lger Hung Fung ook Co, Lt (p85 Q6) 7 Ftorise Hene fin the generl solution of the eqution 4 New Senior Seonr Mthemtis in tion Moule lger n Clulus (p6 Q4) 8 If, n C re interior ngles of tringle, show tht osc os osc os os os 4 os os os C rekthrough lger Pure Mthemtis YL Ng & KM Png Chpter Emple 4 p Ftorise Pge
3 os Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 ( ) ( ) os( ) ( ) os( ) ( ) os os os( ) ( ) os [( ) ( ) os( ) os( )] [os( ) os( ) ( ) ( )] os( ) os( ) os os ( ) 4 epn long r row 4 4 (C C C ; C C C ) ( ) 4 ( )( 4) ( )( ) or ± 5 ( ) ( ), oftor epnsion long the r row ( ) 4 (C C C ; C C C ) ( )( ) 4 ( )( )( 6), or 6, oftor epnsion long the st row Pge
4 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge 4 4 LHS ( ; ) ( is ientil to ) 5 LHS ( ) 6 (C C C C ) (C C C, C C C ) ( ) 4 7 (C C C ; C C C ) (Coftor epnsion long the st row) ( )( )[ ( ) ( )( )]( ) ( )( )( )( ) ( )( )( )( )
5 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge 5 8 Let,, Then,, (, ) (C C C ) ( ) (C C C ) ( ) (C C C ) ( ) (C C C C ) 4 4( )( )( )
6 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge 6 Metho Let f (,, ), then f (,, ) f (,, ) f (,, ) f (,, ) f (,, ) is li epression of egree f (,, ) 8 ( ) ( ) is ftor smmetr, n re ftors f (,, ) k( )( )( ) f (,, ) k k 4 f (,, ) 4( )( )( ) 9 ( )( )( ) ( ) ( ) (, )
7 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge 7 (C C C C ) (Coftor epnsion long the n row) ( )( )( ) ( ) ( )( )( )( )( ) (, ) (Coftor epnsion long the r olumn) ( )( )( )( )( ) ( )( )( )( )( ) ( )( )( )( )( )( ) ( )( )( )( )( )( ) (C C C, C C C ) ( )( )( ) ( )( )( )
8 4 os os os os Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 ( ) os( C) os( C ) ( ) os( C) os( C ) ( ) os( C) os( C ) osc os( C) os osc os os( C ) ( ) os os os C os( C) os C os os( C ) ( ) os os os os os C C C os os (, ) osc os C osc C ( C) os C C os os C C os os os C C os ( C) os 4 C C os C C os os 4 C 4 C 4 C osc osc osc ( C) os os C os C os C C os C osc os 4 C ( os C os ) C Pge 8
9 5 os os Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 os os os( ) ( ) os os os( ) ( ) os os os os os os os os( ) os os( ) ( ) os os os os os os os os os( ) os( ) ( ) os os os os os os os os ( ) ( ) ( ) os os os (, ) os os os os os os os os os 6 os os ( os os os ) os os ( os ) os os os os os ( α) ( α) ( β) ( β) ( γ) ( γ) (Coftor epnsion long the r olumn) (γ β) (α γ) (β α) whih is inepenent of Pge 9
10 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 7 (C C C, C C C ) ( )( ) ( )( ) (C C C ) ( )( )( )( ) Let,,, then ( )( )( )( ),, or Pge 4 (rejete), ( ), (rejete) or π nπ, n π, where n is n integer or no solution (Q < ) 8 C osc os osc os os osc os os C os os osc os os os osc os osc os o C os 8 C os osc epn long os( 8 C) r olumn o os osc C [ os( C) os os C] C (os os C C os os C) C (4 os os C 4 C os os C C) 4 ( C os os C) os os C 4 os( C) os os C 4 os(8 ) os os C 4 os os os C 4
11 Determinnt Emples Crete Mr Frnis Hung Lst upte: ugust 5 Pge 9 (n then ivie the whole eterminnt ) (Tke out the ommon ftor from the first olumn) (, ) ( ) (ftorition of ) (oftor epnsion out the first olumn) [ ]
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