FINAL EXAM ~T't06 Focus PR~tTICE
~ a, ~olve -4-ht tqllOtion ~ec•~ t I = for -2... o•, x, ~60•
+anx
cosec-:1-x. + \ = 2--
+an 'X.
tao x • I ton ?C. • I/';)
Cl t cot.,?C.) ti • 2-
tan ?C. X • tQn-•c 1) ,c,. • ton ·• ( ''=>)
., 3 -x. • 45° ~ s ':>&. sr•
cot
( +on':17G
2:
__!_ +-:i-2-
tm:x.
+t+ 1 • :rc;;,;_
I t :>tan,::t - '3-tqn x
so)xtan°,c,
=o
+
Gl: ~s·
0
Q3: IS0°+"1S • ':>:>5°
+
QI-= 'JG.51- 0
I Q'j c 180°+ :>6.ST 0 & 'J06.ST 0
let u -= +an ')(,
-~ ~ = Lfs: 'JG. ST , -:>:>S~ ':>06.'H· 0
0
lt':lU,-3usQ
'::>U:i-3utl-=O
cu-I) ( :>u-1) so
U=l . u .. y:>
+an X :l ,tan x"V:l
b) Prove +hat tan?K. (eos- 'lcosx-9tC 'X.) 1: ')sin 'X.
+an 'JX (-:,cosx - secx) ~ 9in 'J~ ( I )
-- -:>cosx--
cos 'J~ C.OS.t
-= ':)~inxcos~ (-:icos"x-1)
COi'J~ C~?G
rr 'lS in ? C ~ ( co--:rx)
~:t ~
-=':>sin ?l , proven'·
I. A straight line 9x. +'ly c 10 intersec~ q cur"e ~ - fy s -::, Qt two point~, P Qnd ~ .
Find the coordinate~ of' the points , P Qtl d G.
t;ub X-=3,?l-=-5 into (i)
'3
-:,y -:: 10 - 37' y:S-~'.X'
1J = s-¾ X ---© Y=S-~(!?i) Y=S-~(-5)
.9. 2 ~ -~
- :)'3 --@
y:: 3 ~:: ':)~
X
~hJb (D into @ .·. , coordinQte P and Q Qre ~
.9.._ 5 .,-'J _ __,, 90-3'J7C. = -':>(IOX-3-x,2 ) (-S, ~ )<(~ (3, '$)
X -:>(S - 1/:, x.)
qo - 3':>x. = -':>o:t +G,c, :i
q 5
---=-'J
'X. 10-37' 6Xi'+ l':>:t-90 = 0
<=\(10-'3~) - SC?<.)= -'J (X - 3)(-x.+S) =0
?C.(I0-3X) 'X.-c~ '?(.-c -5
qo - :>":f~ -5x
---=--=-
IO?C..-'3?l:i
--'J - -~
-
~ a, ~olve -4-ht tqllOtion ~ec•~ t I = for -2... o•, x, ~60•
+anx
cosec-:1-x. + \ = 2--
+an 'X.
tao x • I ton ?C. • I/';)
Cl t cot.,?C.) ti • 2-
tan ?C. X • tQn-•c 1) ,c,. • ton ·• ( ''=>)
., 3 -x. • 45° ~ s ':>&. sr•
cot
( +on':17G
2:
__!_ +-:i-2-
tm:x.
+t+ 1 • :rc;;,;_
I t :>tan,::t - '3-tqn x
so)xtan°,c,
=o
+
Gl: ~s·
0
Q3: IS0°+"1S • ':>:>5°
+
QI-= 'JG.51- 0
I Q'j c 180°+ :>6.ST 0 & 'J06.ST 0
let u -= +an ')(,
-~ ~ = Lfs: 'JG. ST , -:>:>S~ ':>06.'H· 0
0
lt':lU,-3usQ
'::>U:i-3utl-=O
cu-I) ( :>u-1) so
U=l . u .. y:>
+an X :l ,tan x"V:l
b) Prove +hat tan?K. (eos- 'lcosx-9tC 'X.) 1: ')sin 'X.
+an 'JX (-:,cosx - secx) ~ 9in 'J~ ( I )
-- -:>cosx--
cos 'J~ C.OS.t
-= ':)~inxcos~ (-:icos"x-1)
COi'J~ C~?G
rr 'lS in ? C ~ ( co--:rx)
~:t ~
-=':>sin ?l , proven'·
I. A straight line 9x. +'ly c 10 intersec~ q cur"e ~ - fy s -::, Qt two point~, P Qnd ~ .
Find the coordinate~ of' the points , P Qtl d G.
t;ub X-=3,?l-=-5 into (i)
'3
-:,y -:: 10 - 37' y:S-~'.X'
1J = s-¾ X ---© Y=S-~(!?i) Y=S-~(-5)
.9. 2 ~ -~
- :)'3 --@
y:: 3 ~:: ':)~
X
~hJb (D into @ .·. , coordinQte P and Q Qre ~
.9.._ 5 .,-'J _ __,, 90-3'J7C. = -':>(IOX-3-x,2 ) (-S, ~ )<(~ (3, '$)
X -:>(S - 1/:, x.)
qo - 3':>x. = -':>o:t +G,c, :i
q 5
---=-'J
'X. 10-37' 6Xi'+ l':>:t-90 = 0
<=\(10-'3~) - SC?<.)= -'J (X - 3)(-x.+S) =0
?C.(I0-3X) 'X.-c~ '?(.-c -5
qo - :>":f~ -5x
---=--=-
IO?C..-'3?l:i
--'J - -~
-
