M@theMagicS

Home for Number Wizards

TRIGNO 1
Class 11 - Mathematics
Time Allowed: 2 hours Maximum Marks: 40

1. If cot (α + β) = 0 , then sin (a + 2β) is equal to [1]

a) sin α b) cos α

c) cos 2β d) sin 2α

2. The value of cos is [1]

41π

a) −√3
b) √3

2 2

c) 1
d) −1

√2 √2

3. (sin 105° + cos 105°) = ? [1]

a) 1
b) 1

√3 √2

–
c) 2
d) √2
√3

−−−−−
4. If π < x < 2π , then √ 1+cos x
is equal to [1]
1−cos x

a) - cosec x - cot x b) - cosec x + cot x

c) cosec x - cot x d) cosec x + cot x

5. If tan θ = , then sin θ is [1]
−4

a) not - b) or
4 4 −4 4

5 5 5 5

c) −4

5
but not 4

5
d) 4

5
but not - 4

6. If tan θ 1 tan θ2 = k , then

cos(θ1 −θ2 )
= [1]
cos(θ1 +θ2 )

a) k−1

k+1
b) 1−k

1+k

c) d)
k+1 1+k

k−1 1−k

7. tan 5π

4
=? [1]

a) 1
b) 1
√3

–
c) √3 d) -1
8. 2 sin
5π

12
sin
π

12
=? [1]
–
a) 1
b) √2
√2

c) √3
d) 1

2
2

9. cos(
π

4
+ x) + cos(
π

4
− x) =? [1]
–
a) √2 cos x b) 2 cos x

1/5
Contact - Navpreet Arora 9907521106
 –
c) 2 sin x d) √2 sin x

10. The value of cot( π

+ θ) cot(
π
− θ) [1]
4 4

a) -1 b) 1

c) Not defined d) 0
∘ ∘

11. cos 10 +sin 10

∘ ∘
is equal to [1]
cos 10 −sin 10

a) -tan 35o b) tan 55o

c) cot 55o d) -cot 35o

∘ ∘ ∘ ∘

[1]
sin(180 +θ) cos(90 +θ) tan(270 −θ) cot(360 −θ)
12. sin(360
∘
−θ) cos(360
∘
+θ) cosec(−θ) sin(270
∘
+θ)
=?
–
a) √3
b) √2
2

c) 1 d) 3

13. The value of sin π

18
+ sin
π

9
+ sin
2π

9
+ sin
5π

18
is given by [1]

a) sin 7π

18
+ sin
4π

9
b) cos
π

9
+ sin
π

c) cos π

6
+ cos
3π

7
d) 1
14. cos
2π

3
cos
π

4
− sin
2π

3
sin
π

4
=? [1]

a) (√3+1)
b) −(√3+1)

√2 √2

c) (√3+1)
d) −(√3+1)

2√2 2√2

15. sin 36° = ? [1]

a) √10+2√5 b) (√5−1)

4
4

c) √10−2√5 d) (2√5−1)

4
4

16. The value of cos 12° + cos 84° + cos 156° + cos 132° is [1]

a) 1 b) 1

c) − 1

2
d) 1

17. If sec x = -2 and π < x <

3π

2
, then sin x = ? [1]

a) −√3
b) −1

2
2

c) 1

2
d) √3

18. tan 11π

6
=? [1]
–
a) − √3 b) 1

√3

–
c) −1
d) √3
√3

[1]
cos(π+θ) cos(−θ)
19. π
=?
cos(π−θ) cos( +θ)
2

a) cot θ b) - cot θ

c) - tan θ d) tan θ
20. sec 150° = ? [1]

2/5
Contact - Navpreet Arora 9907521106
 a) -2 b)
−2

√3

c) 2 d) 2

√3

21. The value of 2cos θ - cos 3θ - cos 5θ -16 cos 3θ sin2 θ is [1]

a) 1 b) -1

c) 2 d) 0
22. tan 150° = ? [1]
– –
a) √3 b) − √3

c) −1
d) 1

√3 √3

23. If tan (A - B) = 1, sec(A + B) = 2

, then the smallest positive value of B is [1]
√3

a) 11π

24
b) 25π

24

c) 19π

24
d) 13π

24

cos 6x+cos 4x
24. sin 6x−sin 4x
=? [1]

a) cot x b) tan x

c) - tan x d) - cot x
25. If cos x = 3

5
and x lies in quadrant IV, then find the values of cosecx + cotx. [1]
–
a) √3 b) -8
−1
c) √3
d) -2

26. sin
π

4
cos
π

12
+ cos
π

4
sin
π

12
=? [1]
–
a) b)
1
√2
2

–
c) √3
d) 2√2
2

27. Mark the Correct alternative in the following: The value of tan x sin( cos( is [1]
π π
+ x) − x)
2 2

a) 1 b) -1

c) None of these d) sin 2x

1

28. If cos θ = and cos ϕ = , where θ and ϕ both lie in quadrant IV, then sin (θ + ϕ) = ? [1]
4 12

5 13

−16 −33
a) 65
b) 65

−56
c) 16

65
d) 65

29. (sec θ − cos θ) (cosec θ − sin θ) (cot θ + tan θ) =? [1]

a) 2 b) 0

c) 1 d) -1
30. Which of the following is not possible? [1]
2

A. cos θ =
1+t
,t ≠ 0
2
1−t

B. sin θ = 5

C. tan θ = 100

D. sec θ =
5

3/5
Contact - Navpreet Arora 9907521106
 a) C b) D

c) B d) A

31. 2(1 - 2 sin2 7x) sin 3x is equal to [1]

a) cos 17x + cos 11x b) sin 17x + sin 11x

c) cos 17x - cos 11x d) sin 17x - sin 11x

32. If sin θ = and cos ϕ = , where θ and ϕ both lie in quadrant I, then sin (θ + ϕ) = ? [1]
15 12

17 13

a) b)
180 171

221 221

c) 220

221
d) 181

221

33. cos 50° cos 10° - sin 50° sin 10° = ? [1]

a) 1 b) 1

√2

c) √3
d) 1

2
2

34. cos 2θ cos 2ϕ + sin2 2

(θ − ϕ) − sin (θ + ϕ) is equal to [1]
[Hint: Use sin2 A - sin2 B = sin (A + B) sin (A - B)]

a) cos 2(θ − ϕ) b) cos 2(θ + ϕ)

c) sin 2(θ − ϕ) d) sin 2(θ + ϕ)

–
35. If cot θ = √5 and θ does not lie in quadrant I, then the values of cosec θ and sec θ are respectively. [1]
−
− −−
a) √–
6, − √
6
b) –
− √6, − √
6

5 5

−
− −
−
c) − √–
6, √
6
d) –
√6, √
6

5 5

36. The greatest value of sin x cos x is [1]

a) 1 b)
√3

c) 1

2
d) 1

√2

37. cos( 75 ) =
∘
[1]
– – – –
a) (− √3 − 1)/2√2 b) ( √3 + 1)/2√2

– – – –
c) ( √3 − 1)/2√2 d) (1 − √3)/2√2

sin A−sin C
38. If A, B, C are in A.P., then cos C −cos A
= [1]

a) tan B b) tan 2B

c) cot B d) tan 3B
1−cos β
39. Mark the correct alternative in the following: If tanα = , then [1]
sin β

a) tan 2α = tanα b) tan 3α = tan 2β

c) tanβ= tan2α d) tan2β= tan2α

40. sin 5x

sin x
is equal to [1]

a) 16 cos4 x +12 cos2 x + 1 b) 16 cos4 x +12 cos2 x - 1

c) 16 cos4 x -12 cos2 x - 1 d) 16 cos4 x -12 cos2 x + 1

4/5
Contact - Navpreet Arora 9907521106
 5/5
Contact - Navpreet Arora 9907521106