Trigonometry

ANDHERI / BORIVALI / DADAR / CHEMBUR / THANE / MULUND/ NERUL / POWAI

IIT – JEE 2015 TIME: 1HR

TW TEST TOPIC: TRIGONOMETRY

MARKS: 90 DATE: 09/08/13

SINGLE CHOICE QUESTIONS (+3, –1) 1.

The value of the expression1

sin 2 y 1  cos y sin y   is equal to1  cos y sin y 1  cos y

(A) 0 2.

(B) 0

(C) 1

(D) None of these

(B) 2

(C) –1

(D) –2

(B) – cos 2 

(C) sin 2 

(D) – sin 2 

 4

If A – B = , then (1 + tan A) (1 – tan B) = (A) 1

4.

(D) cos y

cosA + sin (270º+A)– sin (270º–A)+ cos (180º + A) = (A) – 1

3.

(C) sin y

(B) 1

1 – 2 sin2      = 4

(A) cos 2 



5.

A quadratic equation whose roots are cos ec2  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 (A) 

7.

a b

(B) 

b a

(C) a 2  b 2

(D) None of these

(B) cot4 

(C) cot3 

(D) 2 cot 

(C) 2

(D) None of these

cos 52° + cos 68° + cos 172° = (A) 0

9.

 2 

3cos θ  cos 3θ is equal to3sin θ  sin 3θ

(A) 1 + cot2  8.

  cos  – cos = b, then tan   is equal to-

(B) 1

If triangle ABC,  C = (A)

3 4

(B)

2 , 3

3 2

then the value of cos2A + cos2B – cos A . cos B is equal to(C)

1 2

(D)

1 4

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

10.

If sin  = n sin (  + 2  ), then tan (  +  ) is equal to (A)

11.

1 n tan  2n

1 n tan  1 n

(C) tan 

(D)

1 n tan  1 n

The product cot123.cot133.cot137 .cot147  , when simplified is equal to: (B) tan 37

(A) 1

12.

(B)

If



is

eliminated

from

(C) cot 33

the

(D) 1

x  a cos     

equations

and

y  b cos     

then

x 2 y 2 2xy   cos      is equal to a 2 b 2 ab

13.

(A) sec 2     

(B) cos ec 2     

The value of 4 cos

    3sec  2 tan is equal to 10 10 10

(A) 1

(B)

5 1

(C) cos 2     

(C)

5 1

(D) sin 2     

(D) zero

1  x2  x and tan   2  x  0,1 , where 0  ,   , then tan      has the 2 x  x 1 2x  2x  1 2 value equal to: (A) 1 (B) 1 (C) 2 (D) 3 4

14.

If tan  

15.

The graphs of y  sin x, y  cos x, y  tan x & y  cos ec 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 1 2

(C)

2

(D)

5 1 2 P

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

17.

(C) 2 2

(D) 3

Q

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 100 (A) 25 2  3 (B) 25 2  3 (C) 25 (D) 2 3



18.

(B) 2







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

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

R

19.

Which of the following is equal to sec  t   tan  t  ?  t  (A) cot      2 4

 t  (B) cot    2 4

(C)

1   cot   t   2 2 

(D) None of these

2

20.

  sin120 The value of  is       16 cos15 .cos30 .cos120 .cos 240  (A)

2 3 8

(B)

3 1 4

(C)

2 3 4

(D) 2  3

21.

Exact value of cos2 73  cos2 47  sin 2 43  sin 2 107 is equal to (A) 1 2 (B) 3 4 (C) 1 (D) none

22.

If x  cos 4 5 1 2 2

(A) 23.

25.

(B) only b

x  cos ec x  sin x then tan 2 x 2  2

(A)

5 1

(C)

3 1 2 2

2x 1 x2

(B)

5 1

(C) a & b

(C)

5 2

(D)

 4

(D)

52

(B)

 x 2 2x

(C) 7 x

(D) 2x

If cos A  1 7 and cos B  13 14 0  A, B   2 then A  B  ________ (B)  3

(C)  4

(D)  6

(C) 4

(D) 5

If K  sin18  cos 36   5 then K  (A) 2 5

(B)

5 2

cos A cos B 1    ,  A, B  0 then 3sin A  6sin B  ______ 3 4 5 2 (A) 0 (B) 3 (C)  4 (D) 6

28.

If

29.

If x 2  Ax  B  0 has tan15 and tan 30 as its roots then A  B  (A) 1

30.

22 4

(D)

If x  tan10 then tan 70 is 

(A)  2 27.

5 1 4

If tan

(A) 26.

(B)

If tan   ab cot   a  b then tan   (A) only a

24.

   sin 4 then x  24 24

(B) 1

(C) 2

(D) 3

If A  B  C  0 then tan A tan B tan 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

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

(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)

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