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sW

W pYi

D t |=yC@Uv

| =FrF


D t |=yC@Uv

| =FrF

u; |=Q@ |D=FrFt O=LD= 'OW=@ CUQO 1=yx}w=R R= |=xR=@ |=Q@ xm |D=FrFt |=yC@Uv |w=UD Qy x@ "1 "OvDUy |OQ@Q=mQB |D=FrFt O=LD= Q}R |w=UD wO p=Ft |=Q@ "Ov} wo|t =yx}w=R sin2  + cos2  = 1 tan  =

sin  cos 

;  6= 0

"O}vm C@=F =Q Q}R OQ@Q=mQB |D=FrFt |=yO=LD= tan   cot  = 1

;  6= 0 ; 90

tan2  + 1 =

;  6= 90

1 cos2  1 cot2  + 1 = sin2 

(hr=

;  6= 0

y @=Q u}= "OvyO|t u=Wv =Q |D=FrFt |=yC@Uv u}@ |x]@=Q |D=FrFt O=LD= GvB u}= '`wtHt QO (? "O}Q=BU@ Q]=N x@ =Q

= x]

"O}@=}@ =Q |D=FrFt |=yC@Uv Q}=U OQwt Qy QO 'OW=@ OvD |x}w=R l} Qo= "2 1 (hr= 5 1 cos = (? 5 1 tan = (G 5 1 cos = (O 5 sin =

"Ov} wo|t =yx}w=R R= |=xR=@ fx j a < x < bg |xawtHt x@ 'OvW=@ OOa wO b w a Qo= "1


"O}Qw; CUOx@ =Q Q}R CQ=@a pY=L 'cot x = 13 Qo= (hr= "3 2 cos x 1 sin x 3 2 3 sin x 3 cos x "O}Qw; CUOx@ =Q Q}R CQ=@a pY=L 'tan x = 34 w OW=@ OvD |=x}w=R x Qo= (? sin x + cos x tan x

1

cos x

+ cos x cot x

"O}vm C@=F =Q Q}R |x]@=Q |DUQO 'Q}R pmW ltm =@

w

cos Cb

=

p

p

tan

2

=

(hr= "4

sin 1 + cos

"O}@=}@ =Q 15 |x}w=R |D=FrFt |=yC@Uv (?

6 + 2 xm s}v=O|t u}vJty &OvDUy OvD ABC ErFt QO Cb w Bb xm s}v=O|t "5 4 p b b "O}@=}@ =Q A |@} QkD Q=Okt '|UOvyt ?=ULu}W=t l} ltm =@ " sin B = 22


2 |@=}xrY=i |=Q@ C=FrFt OwQw |xR=H= '|YwYN s} QL C}=aQ Cra x@ xm s} Q}o@ xR=Ov= =Q 3|@ wvH |v=tDQ=B; `=iDQ= s}y=wN|t "1 B w A |x]kv wO R= "OvDUy u}tR K]U |wQ x]kv wO B w A 'pmW j@=]t $s}Q=Ov =Q u; \=}L x@ CUOx@ 27 w 42 |x}w=R wO w s}vm|t x=ov u=tDQ=B; s=@ x@ OvDUy sy |QDt 19 63 |xrY=i QO xm "O};|t

"O}@=}@ =Q u=tDQ=B; `=iDQ= $s}Q=Ov =Q u; x@ OwQw |xR=H= uOw@ l =vQ]N Cra x@ xm s}@=}@ =Q j}ta ?; p=v=m l} ZQa s}y=wN|t "2 |x}w=R w s}vm|t x=ov p=v=m |wU u; |x}W=L x@ p=v=m |wU u}= |QDt 0 82 |xrY=i R= 'pmW j@=]t |xrY=i u}vJty w OW=@ Owta p=v=m O=ODt= Q@ C w B 'A Q@ xOvQPo \N Qo= "O};|t CUOx@ 18 "O}@=}@ =Q ?; p=v=m ZQa 'OW=@ QDt 1 65 u}tR K]U =D Q_=v sWJ u}@

v= D t y } D }= L QO 'CU= xOW xO=iDU= |UQO ?=Dm |xLiY QO xOW h}YwD |xr}Uw R= xOW xO=O |=yu} QtD QO "2 "O} Q}o@ ltm |UOvyt ?=ULu}W=t R= QO |rw OQ=O Q=Qk xJwm w xv=N |=[i u}@ |@ wvH |=yxv=N \=}L "|@ wvH w |r=tW %OvDUy `wv wO Q@ =yxv=N swta "3 "CU= xDiQo Q=Qk xJwm w \=}L u}@ xv=N |=[i '|r=tW |=yxv=N

O} w | = u Qt u p


u; lwv x@ 'OvDUy CNQO l} hQ] wO QO 'Qo}Oty |QDt 11 6 |xrY=i x@ xm B w A |x]kv wO R= "3 'OvW=@ \Nsy CNQO |=B w B 'A Qo= "O};|t CUOx@ 42 w 36 |=yx}w=R w s}vm|t x=ov CNQO "O}@=}@ =Q CNQO `=iDQ= |x]kv wO pY=i OL QO =Q xJ=}QO l} ZQa s}y=wN|t w s}=xO=DU}= A |x]kv QO 'Q}R pmW j@=]t "4 w OW=@ QDt 68 w QDt 35 ?}DQD x@ C w B \=kv R= A |x]kv |xrY=i Qo= "s} Q}o@ xR=Ov= C w B d |x}w=R u}vJty #Ow@ Oy=wN QOkJ xJ=}QO ZQa 'OwW 43 'BAC u=t|xrY=i xm s}v=O@ s}Q=O CUwO "s}vm|t CmQL xiQ]l} |=xO=H QO |v}W=t QO 'Q}R |xWkv j@=]t "5 u=Q=@ "CU= QOkJ OwW|t xO}O B |x]kv QO xO=H |QDtxO OvJ QO xm |=xtWJ =D A |x]kv R= "O}vm|t O=yvW}B xrY=i uOQm =O}B |=Q@ |WwQ xJ "s} wW xO=}B u}W=t R= s}y=wN|tv w OQ=@|t |O}OW


D t |=yO=LD=

| =FrF

"O}vm C@=F =Q Q}R |D=FrFt |=yO=LD= |DUQO "1 r= ? G O y w R

h

tan + cot =

1

6= 0 ; 90

sin cos 2 + 1 = tan cos2

cos2 (sin + cos )2 = 1 + 2 sin cos

tan2 + cos2

1

cos2 = sin2

sin2

1)(cot + 1) = tan cos2 (2 + tan2 ) = 2 sin2 1 cos sin tan = (tan

; 6= 90

6= 0 ; 90

cot

6= 90 6= 90

cos

"O}vm C@=F =Q Q}R |D=FrFt |=yO=LD= |DUQO "2 r= 1 +cossinx x + 1 +cossinx x = cos2 x ? 1 cot4 x = sin22 x sin14 x 1 1 G sin2 x sin2 y = 1 + tan 2 y 1 + tan2 x tan2 x 6 O cot16 x 3cos 2 x = 1 + tan x

h

x 6= 90 x 6= 0 x; y 6= 90 x 6= 90

"OW Oy=wN |ivt xQ=wty Q}R CQ=@a pY=L xm O}vm C@=F "3 2(sin6 x + cos6 x) 3(sin4 x + cos4 x)


"OW=@ CUQO xW}ty Q}R |=aO= xm O}@=}@ |Qw] =Q c w b 'a O=Oa= "4 sin x cos x sin x + cos x

1

= a sin x + b cos x + c

; x 6= 0 ; 90


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