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

Xi trigonometric functions and identities (t) part 1

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Xi trigonometric functions and identities (t) part 1