Test (elaborations) MATHEMATICS

Trigonometrical Ratios, Functions and Identities
31




Measurement of Angles, Trigonometrical Ratios , Function and
Identities
Basic Level


1. Which of the following relation is correct [WB JEE 1991]

(a) sin 1o  sin 1 (b) sin 1  sin 1o (c) sin 1  sin 1o (d) sin 1  sin 1o
180
2. The radius of the circle whose arc of length 15 cm makes an angle of 3/4 radian at the centre is [K
1 1
(a) 10 cm (b) 20 cm (c) 11 cm (d) 22 cm
4 2
4
3. If tan   , then sin   [Orissa JEE 2002; IIT
3
1979]
4 4 4 4 4 4
(a) but not (b)  or (c) but not  (d) None of these
5 5 5 5 5 5
4. If f (x )  cos 2 x  sec 2 x , then [MNR 1986
(a) f (x )  1 (b) f ( x )  1 (c) 1  f ( x )  2 (d) f ( x )  2
1
5. If x  sec   tan  , then x   [MP PET 19
x
(a) 1 (b) 2 sec  (c) 2 (d) 2 tan 
6. If A lies in the second quadrant and 3 tan A  4  0 then the value of 2 cot A  5 cos A  sin A is equal to [Harayana CEE 1991]
53 7 7 23
(a) (b) (c) (d)
10 10 10 10
7. tan 1o tan 2o tan 3o tan 4 o.......... .. tan 89 o  [MP PET 1998, 2001]
(a) 1 (b) 0 (c)  (d) 1/2
8. The incorrect statement is [MNR 1993
1 1
(a) sin    (b) cos   1 (c) sec   (d) tan   20
5 2
9. If cos   sin   2 sin  , then cos   sin  is equal to [WB JEE 1988]

(a) 2 cos  (b) 2 sin  (c) 2 cos  (d)  2 cos 
10. If sec   tan   p, then tan  is equal to [MP PET 1994]

2p p 1
2
p 1
2
2p
(a) (b) (c) (d)
p2  1 2p 2p p2  1
11. If sin   cos   1, then sin  cos   [Karnataka CET 1998]
(a) 0 (b) 1 (c) 2 (d) 1/2
12. The value of cos 1o cos 2o cos 3 o..... cos 179 o is [Karnataka CET 1999]

, 32 Trigonometrical Ratios, Functions and
Identities
1
(a) (b) 0 (c) 1 (d) None of these
2
1
13. If tan    and  lies in the 1st quadrant, then cos  is [Karnataka
5
1 1 5 5
(a) (b)  (c) (d) 
6 6 6 6
14. If A lies in the third quadrant and 3 tan A  4  0, then 5 sin 2 A  3 sin A  4 cos A  [EAMCET 1994]
24 24 48
(a) 0 (b) (c) (d)
5 5 5
15. (sec 2   1) (cosec 2  1) = [Karnataka CET 1998]

(a) 0 (b) 1 (c) sec  . cosec  (d) sin 2   cos 2 
20
16. If tan   , cos  will be [MP PET 1994]
21
20 1 21 20
(a)  (b)  (c)  (d) 
41 21 29 21
11
17. If cosec A  cot A  , then tan A equal to [Roorkee 1995]
2
21 15 44 117
(a) (b) (c) (d)
22 16 117 43
24
18. If sin   and  lies in the second quadrant, then sec   tan  equal to [MP PET 1997]
25
(a) – 3 (b) – 5 (c) –7 (d) – 9
5 sin   3 cos 
19. If 5 tan   4 , then equal to [Karnataka CET 1998]
5 sin   2 cos 
(a) 0 (b) 1 (c) 1/6 (d) 6
1  cos 
20. equal to [Karnataka CET 1998]
sin 2 
1 1
(a) 0 (b) 1 (c) (d)
1  cos  1  cos 
1
21. The expression simplifies to [SCRA 1999]
tan A  cot A
(a) sec A cosec A (b) sin A cos A (c) tan 2 A (d) sin 2 A
1
22. If for real values of x, cos   x  , then [MP PET 1996]
x
(a)  is an acute angle (b)  is a right angle (c)  is an obtuse angle (d) No value of  is
possible
23. If sin x + cosec x =2, then sinn x  cosec n x is equal to [UPSEAT 2002]
(a) 2 (b) 2 n (c) 2n 1 (d) 2n  2



Advance Level

1
24. One root of the equation cos x  x   0 lies in the interval [H
2
        3 
(a) 0,  (b)   , 0  (c)  ,   (d)  ,
 2  2  2   2 