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JEE Questions for Maths Trigonometric Ldentities And Equations Quiz 3 - MCQExams.com
JEE
Maths
Trigonometric Ldentities And Equations
Quiz 3
The solution of equations cos
2
θ + sin θ + 1 = 0 lies in the interval
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0%
0%
2)
0%
0%
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0%
2)
0%
0%
The number of values of θ in the interval [-π, π] satisfying the equations cos θ + sin 2θ = 0 is
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1
0%
2
0%
3
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4
If cos θ - 4 sin θ = 1, then sin θ + 4 cos θ is equal to
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±1
0%
0
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±2
0%
4
If cos 2χ = (√2 +(cosχ -(1/√2)) , cos χ ≠ 1/2, χ ϵ I
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0%
2)
0%
0%
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0%
2)
0%
0%
If cos x = tan y, cot y = tan z and cot z = tan x , then sin x is equal to
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0%
2)
0%
0%
In a ∆PQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then ∠R is equal to
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5π/6
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π/6
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π/4
0%
3π/4
If cos α + 2cos β + 3cos γ = 0, in α + 2sin β + 3sin γ = 0 and α + β + γ = π then sin 3 α + 8sin 3β + 27 sin 3γ is equal to
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- 18
0%
0
0%
3
0%
9
In a ∆ABC, if ∠A = π/2, then cos
2
B + cos
2
C equals
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- 2
0%
- 1
0%
1
0%
0
Which one of the following is possible
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2)
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tanθ = 45
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If cos 20
o
- sin 20
o
= p, then cos 40
o
is equal to
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P2 √(2 - p2)
0%
P√(2 - p2)
0%
P + √(2 - p2)
0%
P - √(2 - p2)
If S
n
= cos
n
θ + sin
n
θ, then the value of 3S
4
- 2S
6
is given by
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4
0%
0
0%
1
0%
7
If cosχ + cos
2
χ = 1, then the value of sin
12
χ + 3 sin
10
χ + 3 sin
8
χ +sin
6
χ - 1 is
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2
0%
1
0%
- 1
0%
0
sin
2
17.5
o
+ sin
2
72.5
o
is equal to
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cos2 90o
0%
tan2 45o
0%
cos2 30o
0%
sin2 45o
If θ ϵ (0, π/and t
1
= (tan θ)
tan θ
, t
2
= (tan θ)
cot θ
, t
3
= (cot θ)
tan θ
and t
4
= (cot θ)
tan θ
, then
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t1 > t2 > t3 > t4
0%
t4 > t3 > t1 > t2
0%
t3 > t1 > t2 > t4
0%
t2 > t3 > t1 > t4
If 12 cot
2
θ - 31 cosec θ + 32 = 0, the the value of sin θ is
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3/5 or 1
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2/3 or - (2/3)
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4/5 or 3/4
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± 1/2
If sin θ + cosec θ = 2, then the value of sin
10
θ + cosec
10
θ is
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2
0%
210
0%
29
0%
10
If sin θ = sin α, then
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2)
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tan 81
o
- tan 63
o
- tan 27
o
+ tan 9
o
equals
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6
0%
0
0%
2
0%
4
ABCD is trapezium, such that AB and CD are parallel and BC ⊥ CD. If ∠ADB = θ, BC = p and CD = q, then Ab is
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0%
2)
0%
0%
The value of tan 40
o
+ tan 20
o
+ √3 tan 20
o
tan 40
o
is
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√12
0%
1/√3
0%
√3
0%
√3/2
The value of sin 50
o
- sin 70
o
+ sin 10
o
is
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0%
1/√2
0%
0
0%
1
0%
1/2
If tan A and tan B are the roots of abχ
2
- C
2
χ + ab = 0, where a, b and c are the sides of a ∆ABC, then the value of sin
2
A + sin
2
B + sin
2
C is
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0%
1
0%
3
0%
4
0%
2
0%
5
If A + B = 45
o
, then (cot A -(cot B -is equal to
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3
0%
1/2
0%
- 1
0%
- 2
0%
2
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0%
2)
0%
0%
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< 1
0%
= - 1
0%
< 0
0%
None of these
The value of cos
2
(A - B) + cos
2
B - 2 cos(A - B) cos A cos B is
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sin A
0%
sin2 a
0%
cos2 A
0%
cos A
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0%
2)
0%
0%
sin 47
o
+ sin 61
o
- sin 11
o
- sin 25
o
is equal to
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sin 7o
0%
cos 7o
0%
sin 36o
0%
cos 36o
If sin (χ + 3α) = 3 sin(α - χ ), then
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tan χ = tan α
0%
tan χ = tan2 α
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tan χ = tan3 α
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tan χ = 3 tan α
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1/16
0%
- (1/16)
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1
0%
0
If A = 35
o
, B = 15
o
and C = 40
o
, then tan A tan B + tan B tan C + tan C tan A is equal to
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0
0%
1
0%
2
0%
3
If α + β + γ = 2θ, then cos θ + cos (θ - α) + cos (θ - β) + cos (θ - γ ) is equal to
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0%
2)
0%
0%
If sin A + cos B = a and Sin B + cos A = b, then sin (A + B) is equal to
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0%
2)
0%
0%
None of these
If sin A = 1/√10 and sin B = 1/√5, where A and B are positive acute angles, then A + B is equal to
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π
0%
π/2
0%
π/3
0%
π/4
If cos (θ - α) = a and cos (θ - β) = b, then sin
2
(α - β) is equal to
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a2 + b2
0%
a2 - b2
0%
b2 - a2
0%
- a2 - b2
If tan A = 2 tan B + cot B, then 2 tan (A - B) is equal to
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tan B
0%
2 tan B
0%
cot B
0%
2 cot B
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0
0%
1
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2
0%
3
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0
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cos 2θ
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sin 2θ
0%
cos θ
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2)
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0%
0%
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π/3
0%
π/4
0%
0
0%
π/2
sin 120
o
cos 150
o
- cos 240
o
sin 30
o
is equal to
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1
0%
- 1
0%
2/3
0%
If p = cos 55
o
, q = cos 65
o
and r = 175
o
, then the value of
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0
0%
- 1
0%
1
0%
None of these
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tan β + tan γ
0%
2(tan β + tan γ)
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tan β + 2 tan γ
0%
2 tan β + tan γ
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tan 26o
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tan 81o
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tan 51o
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tan 54o
0%
tan 46o
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2
0%
1
0%
0
0%
3
If y = (1 + tan A) (1 - tan B), where A - B = π/4, then (y + 1)
y+1
is equal to
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9
0%
4
0%
27
0%
81
If tan α/2 and tan β/2 are the roots of 8χ
2
- 26χ + 15 = 0, then cos (α + β) is equal to
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627/726
0%
-(627/725)
0%
- 1
0%
None of these
If tan χ = 3/4 , π < χ < 3π/2, then the value of cos χ/2 is
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- (1/√10)
0%
3/√10
0%
1/√10
0%
-(3/√10)
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