Xi trigonometric functions and identities (t) part 1

CLASS XI TRIGONOMETRIC FUNCTIONS AND IDENTITIES WORKSHEET (T)
STHITPRAGYA SCIENCE CLASSES, GANDHIDHAM
ADVANCED MATHEMATICS FOR JEE | BITSAT| GUJCET| OLYMPIADS | IX, X, XI, XII, XII +
MISHAL CHAUHAN (M.Tech, IIT Delhi)
Address 1: Near Gayatri Mandir, Opp. PGVCL Office, Shaktinagar Address 2: Sec-5, G.H.B, Gandhidham
Contact: 9879639888 Email:sthitpragyaclasses@gmail.com
Q 1. If tan  =
1
a
4a
 then sec  - tan  is equal to
(a)
1
2a,
2a
 (b)
1
,2a
2a
 (c) 2a (d)
1
,2a
2a
Q 2. sec2  = 2
4xy
(x y)

, where x  R, y  R, is true if and only if
(a) x + y  0 (b) x = y, x  0 (c) x = y (d) x  0, y  0
Q 3. sin2 
2
(x y)
4xy

 , where x  R, gives real  if and only if
(a) x + y = 0 (b) x = y (c) |x| = |y|  0 (d) none of these
Q 4. cosec 
2 2
2 2
x y
x y



, where x  R, y  R, gives real  if and only if
(a) x = y  0 (b) |x| = |y|  0 (c) x + y = 0, x  0 (d) none of these
Q 5. If sin  + cosec  = 2 then the value of sin8 + cosec8 is equal to
(a) 2 (b) 28 (c) 24 (d) none of these
Q 6. If x = rsin .cos , y = rsin  . sin  and z = rcos  then the value of x2 + y2 + z2 is independent
of
(a) ,  (b) r,  (c) r,  (d) r
Q 7. Let p = a cos  - b sin . Then for all real 
(a) 2 2
p a b
  (b) 2 2
p a b
   (c) 2 2 2 2
a b p a b
     (d) none of
these
Q 8. If 0 <  < 180 then
2 2 2 ..... 2(1 cos )
      ,
there being n number of 2’s, is equal to
(a) n
2cos
2

(b) n 1
2cos
2 

(c) n 1
2cos
2 

(d) none of these
Q 9. The value of tan 2tan
16 8
 
 + 4 is equal to
(a) cot
8

(b) cot
16

(c) cot 4
16

 (d) none of these
Q 10. The value of sin 78 - sin 66 - sin 42 + sin 6 is

(a)
1
2
(b) 
1
2
(c) -1 (d) none of these
Q 11. The value of 3 cosec 20 - sec 20 is equal to
(a) 2 (b) 4 (c)
o
o
sin20
2.
sin40
(d)
o
o
sin20
4.
sin40
Q 12. The maximum value of 1 sin 2cos
4 4
 
   
     
   
   
for real values of  is
Q 13. The minimum value of cos 2 + cos  of real values of  is
(a)
9
8
 (b) 0 (c) -2 (d) none of these
Q 14. The value of cosec 10 - o
3 sec10 is equal to
(a)
1
2
(b) 2 (c) 4 (d) 8
Q 15. The least value of cos2 - 6 sin . cos  + 3 sin2  + 2 is
(a) 4 10
 (b) 4 10
 (c) 0 (d) none of these
Q 16. If cos4  . sec2 ,
1
2
and sin4  .cosec2  are in AP then
cos8  . cos6 ,
1
2
and sin8  . cosec6  are in
(a) AP (b) GP (c) HP (d) none of these
Q 17. If tan ,
9

x and
5
tan
18

are in AP and tan
9

, y and
7
tan
18

are also in AP then
(a) 2x = y (b) x > y (c) x = y (d) none of these
Q 18. If cos(x – y), cos x and cos(x + y) are in HP then
y
cosx.sec
2
equals
Q 19. If 2 sin . cos  . sin  = sin  . sin( + ) then tan , tan  and tan  are in
(a) AP (b) GP (c) HP (d) none of these
Q 20. If tan  = a , where a is a rational number which is not a perfect square, then which of the
following is a rational number ?

(a) sin 2 (b) tan 2 (c) cos 2 (d) none of these
Q 21. Let f() =
cot
1 cot

 
and
5
4

    . Then the value of f() . f() is
(a) 2 (b)
1
2
 (c)
1
2
(d) none of these
Q 22. If tan
2

and tan
2

are the roots of the equation 8x2 – 26x + 15 = 0 then cos( + ) is equal to
(a)
627
725
 (b)
627
725
(c) -1 (d) none of these
Q 23. If sin  + sin  = a and cos  –  = b then tan
2
  
is equal to
(a)
a
b
 (b)
b
a
 (c) 2 2
a b
 (d) none of these
Q 24. If 0 <   <
4

, cos ( + ) =
3
5
and ( – ) =
4
5
then sin 2 is equal to
Q 25. If cos
1 1 1 1
x ,cos y
2 x 2 y
 
 
     
 
 
   
then cos( – ) is equal to
(a)
x y
y x
 (b)
1
xy
xy
 (c)
1 x y
2 y x
 

 
 
(d) none of these
Q 26. If
2sin 1 sin cos
then
1 sin cos 1 sin
   
 
     
is equal to
(a)
1

(b)  (c) 1 –  (d) 1 + 
Q 27. If |tan A| < 1, and |A| is acute then
1 sin2A 1 sin2A
1 sin2A 1 sin2A
  
  
is equal to
(a) tan A (b) –tan 3 (c) cot A (d) –cot A
Q 28. tan .tan .tan
3 3
 
   
    
   
   
is equal to
(a) tan 2 (b) tan 3 (c) tan3  (d) none of these

Q 29. The set of all possible values of  in [–, ] such that
1 sin
1 sin
 
 
is equal to sec  – tan  is
(a) 0,
2

 


 
(b) 0, ,
2 2
 
   
 
  

   
(c) [ –, 0] (d) ,
2 2
 
 
 
 
Q 30. For all real values of , cot  – 2cot 2 is equal to
(a) tan 2 (b) tan  (c) –cot 3 (d) none of these
Q 31. Let a = cos A + cos B – cos (A + B) and b =
A B A B
sin sin cos
2 2 2

. Then a – b is equal to
(a) 1 (b) 0 (c)  1 (d) None of these
Q 32. If tan tan tan k
3 3
 
   
       
   
   
3 then k is equal to
(a) 1 (b) 3 (c)
1
3
(d) none of these
Q 33. If asec  – ctan  = d and bsec  + dtan  = c then
(a) a2 + c2 = b2 + d2 (b) a2 + d2 = b2 + c2 (c) a2 + b2 = c2 + d2 (d) ab = cd
Q 34. If cos 20 – sin 20 = p then cos 40 is equal to
(a) 2
p 2 p
  (b) 2
p 2 p
 (c) 2
p 2 p
  (d) none of these
Q 35. If 3sin  + 4cos  = 5 then the value of 4sin  – 3cos  is
Q 36. If cos 2x + 2cos x = 1 then sin2 x(2 – cos2x) is equal to
(a) 1 (b) –1 (c) 5
 (d) 5
1a 2b 3c 4d 5a 6a 7c 8a 9b 10b
11b 12c 13a 14c 15b 16a 17a 18c 19c 20c
21c 22a 23b 24a 25c 26b 27c 28b 29d 30b
31a 32b 33c 34b 35a 36a

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