Trigonometry

CENTERS: MUMBAI / DELHI / AKOLA / KOLKATA / LUCKNOW / NASHIK / GOA

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI IIT – JEE 2015 TW TEST MARKS: 90 TIME: 1HR TOPIC: TRIGONOMETRY DATE: 09/08/13

SINGLE CHOICE QUESTIONS (+3, –1)

1. The value of the expression-

2sin y 1 cos y sin y1

1 cos y sin y 1 cos y

is equal to-

(A) 0 (B) 1 (C) sin y (D) cos y

2. cosA + sin (270º+A)– sin (270º–A)+ cos (180º + A) = (A) – 1 (B) 0 (C) 1 (D) None of these 3. If A – B =

4 , then (1 + tan A) (1 – tan B) =

(A) 1 (B) 2 (C) –1 (D) –2

4. 1 – 2 sin2

4

=

(A) cos 2 (B) – cos 2 (C) sin 2 (D) – sin 2 5. A quadratic equation whose roots are 2cosec and sec2 , can be -

(A) x2 – 2x + 2 = 0 (B) x2 – 3x + 3 = 0 (C) x2 – 5x + 5 = 0 (D) x2 + 4x – 4 = 0

6. If sin + sin = a and cos – cos = b, then tan

2is equal to-

(A) ab

(B) ba

(C) 2 2a b (D) None of these

7. 3cosθ cos3θ3sin θ sin 3θ

is equal to-

(A) 1 + cot2 (B) cot4 (C) cot3 (D) 2 cot 8. cos 52° + cos 68° + cos 172° = (A) 0 (B) 1 (C) 2 (D) None of these

9. If triangle ABC, C =3

2 , then the value of cos2A + cos2B – cos A . cos B is equal to-

(A) 43 (B)

23 (C)

21 (D)

41


10. If sin = n sin ( + 2 ), then tan ( + ) is equal to -

(A) 1 n tan2 n

(B) 1 n tan1 n

(C) tan (D) tan

n1n1

11. The product cot123 .cot133 .cot137 .cot147 , when simplified is equal to:

(A) 1 (B) tan 37 (C) cot33 (D) 1

12. If is eliminated from the equations x a cos and y b cos then

2 2

2 2

x y 2xy cosa b ab

is equal to

(A) 2sec (B) 2cos ec (C) 2cos (D) 2sin

13. The value of 4cos 3sec 2 tan10 10 10 is equal to

(A) 1 (B) 5 1 (C) 5 1 (D) zero

14. If 2

2

x xtanx x 1

and 2

1tan x 0,12x 2x 1

, where 0 ,2

, then tan has the

value equal to: (A) 1 (B) 1 (C) 2 (D) 3 4 15. The graphs of y sin x, y cos x, y tan x & y cosec x are drawn on the same axes from 0 to 2 .

A vertical line is drawn through the point where the graphs of y cos x & y tan x cross, intersecting the other two graphs at points A & B. The length of the line segment AB is:

(A) 1 (B) 5 12 (C) 2 (D) 5 1

2

16. The right-angled triangle has two circles touching its sides as shown. If the angle

at R is 60 and the radius of the smaller circle is 1, then the radius of the larger circle is

(A) 2 3 (B) 2 (C) 2 2 (D) 3 17. An equilateral triangle, with sides of 10 inches, is inscribed in a square ABCD in such a way that one

vertex is at A, another vertex on BC and one on CD. The area of the square is

(A) 25 2 3 (B) 25 2 3 (C) 25 (D) 1002 3

18. The value of the expression 2 2 2 2sin 1 sin 2 sin 3 ..... sin 90 , is (A) 0 (B) 45 (C) 45.5 (D) 90

P

Q R


19. Which of the following is equal to sec t tan t ?

(A) tcot2 4

(B) tcot2 4

(C) 1 cot t2 2

(D) None of these

20. The value of 2

sin12016cos15 .cos30 .cos120 .cos 240

is

(A) 2 38 (B) 3 1

4 (C) 2 3

4 (D) 2 3

21. Exact value of 2 2 2 2cos 73 cos 47 sin 43 sin 107 is equal to (A) 1 2 (B) 3 4 (C) 1 (D) none

22. If 4 4x cos sin24 24

then x

(A) 5 12 2 (B) 5 1

4 (C) 3 1

2 2 (D) 2 2

4

23. If tan abcot a b then tan

(A) only a (B) only b (C) a & b (D) 4

24. If xtan cosec x sin x2 then 2tan x 2

(A) 5 1 (B) 5 1 (C) 5 2 (D) 5 2

25. If x tan10 then tan 70 is

(A) 2

2x1 x

(B) 2x

2x (C) 7 x (D) 2x

26. If cos A 1 7 and cos B 13 14 0 A,B 2 then A B ________

(A) 2 (B) 3 (C) 4 (D) 6

27. If K sin18 cos36 5 then K

(A) 2 5 (B) 5 2 (C) 4 (D) 5

28. If cos A cos B 13 4 5

, A, B 02

then 3sin A 6sin B ______

(A) 0 (B) 3 (C) 4 (D) 6

29. If 2x Ax B 0 has tan15 and tan 30 as its roots then A B

(A) 1 (B) 1 (C) 2 (D) 3

30. If then tan A tan Btan C

(A) tan A tan B tan C (B) tan A tan B tan C

(C) tan C tan A tan B (D) none of these

A B C 0


(STM Sir) TRIGONEMETRY (ANSWER KEY)

1. (d) 2. (b) 3. (b) 4. (d) 5. (c)

6. (b)(bonus) 7. (c) 8. (a) 9. (a) 10. (d)

11. (d) 12. (d) 13. (d) 14. (a) 15. (a)

16. (d) 17. (b) 18. (c) 19. (a)(bonus) 20. (c)

21. (c) 22. (c) 23. (c)(bonus) 24. (c) 25. (b)

26. (b) 27. (a) 28. (d) 29. (b) 30. (c)

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Trigonometry