Baixe 65879251 - Trigonometric - Rations - amp - Fns - Qns e outras Exercícios em PDF para Matemática, somente na Docsity!
QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
1. If sinA = 1 10
& sinB = 1 5
, where A and B are positive acute angles, then A + B =
(A) π (B) π 2
(C) π 3
(D) π 4
2. If sin θ + cos θ = m and sec θ + cosec θ = n, then n (m + 1) (m - 1) = (A) m (B) n (C) 2m (D) 2n 3. If sinA + sinB = C, cosA + cosB = D, then the value of sin (A + B) =
(A) CD (B) CD C 2 +D^2
(C) C^ D C D
2 2 2
+ (D) 2
2 2
CD
C +D
4. If sin A = sin B and cos A = cos B, then :
(A) sin A^ −B 2
= 0 (B) sin A^ +B 2
(C) cos A^ −B 2
= 0 (D) cos (A + B) = 0
5. If f(x) = cos^2 x + sec^2 x, then : (A) f(x) < 1 (B) f(x) = 1 (C) 1 < f(x) < 2 (D) f(x) ≥ 2 6. If α + β − γ = π, then sin^2 α + sin^2 β − sin^2 γ = (A) 2 sin α sin β cos γ (B) 2 cos α cos β cos γ (C) 2 sin α sin β sin γ
(D) None of these
7. cos^2 48º - sin^2 12º =
(A) 5 1 4
− (B) 5 1
(C) 3 1
− (D) 3 1
8. sin^6 θ + cos^6 θ + 3 sin^2 θ cos^2 θ = (A) 0 (B) - 1 (C) 1 (D) None of these 9. 1 + cos 2x + cos 4x + cos 6x = (A) 2 cos x cos 2x cos 3x (B) 4 sin x cos 2x cos 3x (C) 4 cos x cos 2x cos 3x (D) None of these 10. sin 75º =
(A) 2 3 2
− (B) 3 1
(C)
(D) 3 1
11. sin 20º sin 40º sin 60º sin 80º =
(A) - 3 16
(B) 5
(C) 3
(B) - 5
12. If x - sec θ + tan θ, then x + 1 x
(A) 1 (B) 2 sec θ (C) 2 (D) 2 tan θ
13. sin 12º sin 48º sin 54º =
(A) 1 16
(B) 1
Trigonometry Ratios and Functions
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(C) 1
(D) 1
cos sin cos sin
sin cos
(A) 1 (B) - 1
(C) 0 (D) None of these
15. tan 3A - tan 2A - tan A = (A) tan 3A tan 2A tan A (B) - tan 3A tan 2A tan A (C) tan A tan 2A - tan 2A tan 3A - tan 3A tan A (D) None of these 16. 3 sin^4 sin^4 (^ )
^ π^ −α 3 π α ^
^
2 sin^6 2 sin^6 (^5 ) π (^) +α π α ^
^ +^ −
(A) 0 (B) 1
(C) 3 (D) sin 4α + sin 6 α
17. (sec A + tan A − 1) (sec A − tan A + 1) - 2 tan A = (A) sec A (B) 2 sec A (C) 0 (D) 1 18.^2 1 1
2 2
sin tan ( tan ) sin sin ( tan )
θ θ θ θ θ θ
(A) sin tan
θ 1 + θ
(B) 2
sin tan
θ
(C)
sin ( tan )
θ
(D) None of these
19. If m tan (θ − 30º) = n tan (θ + 120º),
then m^ n m n
(A) 2 cos 2θ (B) cos 2θ (C) 2 sin 2θ (D) sin 2θ
20. 1 + cos 56º + cos 58º - cos 66º = (A) 2 cos 28º cos 29º cos 33º (B) 4 cos 28º cos 29º cos 33º (C) 4 cos 28º cos 29º sin 33º (D) 2 cos 28º cos 29º sin 33º 21. If A + B = 225º, then, cot A 1 + cot A . cot B 1 + cot B
(A) 1 (B) - 1
(C) 0 (D) 1
22. tan^2 θ sec^2 θ (cot^2 θ - cos^2 θ) = (A) 0 (B) - 1 (C) 1 (D) 2 23. tan 9º − tan 27º − tan 63º + tan 81º =
(A) 1 2
(B) 2
(C) 4 (D) 8
24. If tan θ = x x
sin cos
φ 1 − φ and
tan φ =
sin cos
θ − y θ , then
x y =
(A) sin sin
φ θ
(B)
sin sin
θ φ
(C) sin cos
φ 1 − θ (D) sin cos
θ 1 − φ
25.^1 8
^
^
^
^
^
cos π^ cos π^ cos π
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
34. The value of θ lying between 0 &
π 2 and satisfying the equation, 1 4 4 1 4 4 1 4 4
2 2 2 2 2 2
sin cos sin sin cos sin sin cos sin
θ θ θ θ θ θ θ θ θ
(A) 7
π (^) or
π
(B)
π
(C)
π 24
(D) None of these
35. The equation, sec^2 θ = 4 xy 2 (x + y)
is only
possible when : (A) x = y (B) x < y (C) x > y (D) None of these
36. If sin^ cos
2 A 2
a
A
b
a + b , then the
value of sin
8 3
A
a
8 3
A
b
is equal to
(A)
( a + b)^3 (B)^
a b a b
3 3 ( + )^3
(C) a b a b
2 2 ( + )^2 (D)^ None of these
37. The maximum value of, a cos x + b sin x is : (A) a + b (B) a - b (C) a + b (D) (a^2 + b^2 )1/ 38. The value of, sin π 14 sin
π sin
π
sin
π
sin
π
sin
π
sin
π
(A)
(B) 1
(C) 1
(D) 1
39. The angle subtended at the centre of a circle of radius 3 metres by an arc of length 1 metre is equal to : (A) 20º (B) 60º
(C)
3 radian^ (D)^ 3 radians
40. The circular wire of diameter 10 cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to :
(A) π 4
radian (B) π 3
radian
(C) π 5
radian (D) π 10
radian
41. The greatest and least value of, sin x cos x are :
(A) 1, - 1 (B) 1 2
(C) 1
, − (D) 2, - 2
42. If α + β + γ = 2 π, then :
(A) tan α 2
= tan α 2
tan β 2
tan γ 2
(B) tan α 2 tan β 2
- tan β 2 tan γ 2
- tan γ 2 tan α 2 = 1
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QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439
(C) tan α 2
- tan β 2
- tan γ 2 = − tan α 2 tan β 2 tan γ 2 (D) None of these
43. If tan θ − cot θ = a & sin θ + cos θ = b, then (b^2 - 1)^2 (a^2 + 4) is equal to : (A) 2 (B) - 4 (C) ± 4 (D) 4 44. If x sin^3 α + y cos^3 α = sin α cos α and x sin α − y cos α = 0, then x^2 + y^2 = (A) - 1 (B) ± 1 (C) 1 (D) None 45. If sec θ + tan θ = p, then tan θ is equal to :
(A) 2 (^21)
p p −
(B)
p p
(C) p p
+ (D) 2
p p +
46. If tan A = 1 − cos sin
B
B , find tan 2A in terms of tan B and show that : (A) tan 2A = tan B (B) tan 2A = tan^2 B (C) tan 2A = tan^2 B + 2 tan B (D) None of these
47. For 0 < φ < π 2 , if x = n =
∞ ∑ 0
cos2n^ φ,
y = n =
∞ ∑ 0
sin2n^ φ, z = n =
∞ ∑ 0
cos2n^ φ sin2n^ φ,
then : (A) xyz = xz + y (B) xyz = xy + z (C) xyz = x + y + z (D) xyz = yz + x
48. If tan (A + B) = p, tan (A - B) = q, then the value of tan 2A in terms of p and q is :
(A) p q p q
− (B)^
p q p q
(C)
p q p q
(D)
p q p
49. If x = y cos 2 3
π (^) = z cos
π
, then xy + yz + zx = (A) - 1 (B) 0 (C) 1 (D) 2
50. If sin θ 1 + sin θ 2 + sin θ 3 = 3, then cos θ 1 + cos θ 2 + cos θ 3 = (A) 3 (B) 2 (C) 1 (D) 0 51. The value of, cos 12º + cos 84º + cos 156º + cos 132º is :
(A)
2 (B)^1
(C) - 1
(D)
52. If sin (120º − α) = sin (120º − β), 0 < α , β < π, then α & β are given by (A) α = β (B) α = β or α + β = π 3
(C) α + β = 0, α + β =
π 3
(D) None of these
53.
cos sin cos sin
(A) tan 54º (B) tan 36º (C) tan 18º (D) None of these
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