Post on 19-Oct-2020
JEE Mains Super40 Revision Series
TRIGONOMETRY
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1 8646
JEE Mains Super40 Revision Series TRIGONOMETRY
The number of integral values of for which the equation has a solution is (1) (2) (3) (4)
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2 9793
JEE Mains Super40 Revision Series TRIGONOMETRY
The value of is (a) (b) (c) (d)
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3 11683
JEE Mains Super40 Revision Series TRIGONOMETRY
If , then the number of real values of x, which satisfy the equation is : (1) 3 (2) 5 (3) 7 (4) 9
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4 11799 JEE Mains Super40 Revision Series TRIGONOMETRY
If then
k 7 cosx + 5 sinx = 2k + 14 8 10 12
cot(2
∑n= 1
cot − 1(1 +n
∑k= 1
2k))23
25
25
23
23
24
25
26
0 ≤ x < 2πcosx + cos 2x + cos 3x + cos 4x = 0,
sin− 1( ) + sin− 1( ) = 2 tan− 1 x2a
1 + a22b
1 + b2x =
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5 17468
JEE Mains Super40 Revision Series TRIGONOMETRY
, , find
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6 19684
JEE Mains Super40 Revision Series TRIGONOMETRY
If then the value of is: (2) (3)
(4)
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7 22037
JEE Mains Super40 Revision Series TRIGONOMETRY
The equation
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8 22312
JEE Mains Super40 Revision Series TRIGONOMETRY
Let be a positive integer such that Then (b)
c) d)
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9 22360 JEE Mains Super40 Revision Series TRIGONOMETRY
The value of
√2 cosA = cosB + cos3 B √2 sinA = sinB − sin3 B sin(A − B)
5(tan2 x − cos2 x) = 2 cos 2x + 9, cos 4x2
9−
7
9
−3
5
1
3
2 sin2 x = x2 + x− 2; 0cos2 x
2
n + = .sinπ
2n
cosπ
2n
√n
26 ≤ n ≤ 8
4 < n ≤ 8 4 ≤ n ≤ 8 4 < n < 8
(1 + )(1 + )(1 + )(1 + )iscosπ
8
cos(3π)
8
cos(5π)
8
cos(7π)
8
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(a)1/4 (b) 3/4 (c) 1/8 (d) 3/8
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10 22432
JEE Mains Super40 Revision Series TRIGONOMETRY
If , then (a) (b)
(c) (d) none of these
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11 22457
JEE Mains Super40 Revision Series TRIGONOMETRY
If then (a)
(b)
(c)
(d)none of
these
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12 22512
JEE Mains Super40 Revision Series TRIGONOMETRY
The number of solutions of the pair of equations in the interval is
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13 22513 JEE Mains Super40 Revision Series TRIGONOMETRY
Given then for all real (a) (b) (c)
y = , x ∈ (0, )sin4 x − cos4 x + sin2 x cos2 x
sin4 x + cos4 x + sin2 x cos2 x
π
2− ≤ y ≤
3
2
1
2
1 ≤ y ≤1
2− ≤ y ≤ 1
5
3
α + β + γ = 2π,
tan( ) + tan( ) + tan( ) = tan( )tan( )tan( )α
2
β
2
γ
2
α
2
β
2
γ
2
tan( )tan( ) + tan( )tan( ) + tan( )tan( ) = 1α
2
β
2
β
2
γ
2
γ
2
α
2
tan( ) + tan( ) + tan( ) = − tan( )tan( )tan( )α
2
β
2
γ
2
α
2
β
2
γ
2
2 sin2 θ − cos(2θ) = 0, 2 cos2 θ − 3 sin θ = 0 [0, 2π]
A = sin2 θ + cos4 θ, θ, 1 ≤ A ≤ 2 ≤ A ≤ 13
4
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(d)
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14 22518
JEE Mains Super40 Revision Series TRIGONOMETRY
where . Number of pairs of
which satisfy both the equations is 0 (b) 1 (c) 2 (d) 4
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15 22556
JEE Mains Super40 Revision Series TRIGONOMETRY
The general values of satisfying the equation is
(b) (d)
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16 22558
JEE Mains Super40 Revision Series TRIGONOMETRY
The number of solutions of the equation lying in the interval is 0 (b) 1 (c) 2 (d) 3
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17 22611
JEE Mains Super40 Revision Series TRIGONOMETRY
The set of all x in satisfying is given by
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18 22655 JEE Mains Super40 Revision Series TRIGONOMETRY
≤ A ≤ 113
16≤ A ≤
3
4
13
16
cos(α − β) = 1and cos(α + β) = ,l
eα, βμ ∈ [ − π, π]
α, β
θ 2 sin2 θ − 3 sin θ − 2 = 0 (n ∈ Z).
nπ + ( − 1)n π
6nπ + ( − 1)
n π
2nπ + ( − 1)
n 5π
6nπ + ( − 1)
n 7π
6
tanx + secx = 2 cosx[0, 2π]
( , )−π
2
π
2|4 sinx − 1| < √5
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Let Then is (a) only when (b) forall real (c) for all real (d) only when
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19 22690
JEE Mains Super40 Revision Series TRIGONOMETRY
Consider the system of linear equations in Which of the
following can be the value of for which the system has a nontrivial solution
none of these
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20 22696
JEE Mains Super40 Revision Series TRIGONOMETRY
The equation in the variable has real roots.
The can take any value in the interval (a) (b) (c) (d)
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21 22753
JEE Mains Super40 Revision Series TRIGONOMETRY
If no solution of lies on the line then a
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22 22774 JEE Mains Super40 Revision Series TRIGONOMETRY
Let Then the set of all satisfying is
f(θ) = sin θ(sin θ + sin 3θ). f(θ) ≥ 0 θ ≥ 0 ≤ 0θ ≥ 0 θ ≤ 0 θ ≤ 0
x, yandz :(sin 3θ)x − y + z = 0(cos 2θ)x + 4y + 3z = 0 3x + 7y + 7z = 0
θ
nπ + ( − 1)n , ∀n ∈ Zπ
6nπ + ( − 1)n , ∀n ∈ Z
π
3nπ + ( − 1)n , ∀n ∈ Z
π
9
(cos p − 1)x2 + (cos p)x + sin p = 0 x
p (0, 2π) ( − π, 0) ( − , )π
2
π
2(0, π)
3 sin y + 12 sin3 x = a y = 3x,a ∈ ( − ∞, − 9) ∪ (9, ∞) a ∈ [ − 9, 9] aa ∈ { − 9, 9} noneofthese
f(x) = x2andg(x) = sinxf or allx ∈ R. x(fogogof)(x) = (gogof)(x), where(fog)(x) = f(g(x)),±√nπ, n ∈ {0, 1, 2, .} ±√nπ, n ∈ {1, 2, .}
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23 22776
JEE Mains Super40 Revision Series TRIGONOMETRY
For the equation sin has (A)infinitely manysolutions (B)three solutions (C)one solution (D)no solution
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24 22933
JEE Mains Super40 Revision Series TRIGONOMETRY
If then which of the following is not true? (a)
(b) (c) (d) none of these
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25 22959
JEE Mains Super40 Revision Series TRIGONOMETRY
equals a) b) c) d)
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26 23013
JEE Mains Super40 Revision Series TRIGONOMETRY
The value of is (b) (c) (d) none of
these
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+ 2nπ, n ∈ {, − 2, − 1, 0, 1, 2}π
22nπ, n ∈ {, − 2, − 1, 0, 1, 2, }
x ∈ (0, π), sinx + 2 x − sin 3x = 3
= k(k ≠ 1)tan 3A
tanA=
cosA
cos 3A
k − 1
2
=sin 3A
sinA
2k
k − 1=
cot 3A
cotA
1
k
(sec 2x − tan 2x) tan(x − )π
4tan( − x)
π
4cot(x − )
π
4tan2(x + )
π
4
tan[cos − 1( ) + tan− 1( )]4
5
2
3
6
17
7
16
16
7
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27 23080 JEE Mains Super40 Revision Series TRIGONOMETRY
The equation has one negative solution one positive solution no
solution more than one solution
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28 23105
JEE Mains Super40 Revision Series TRIGONOMETRY
Which of the following is the solution set of the equation
(a)(0.1) (b) (c) (d)
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29 23124
JEE Mains Super40 Revision Series TRIGONOMETRY
The value of (b) (c) (d)
independent of
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30 27849
JEE Mains Super40 Revision Series TRIGONOMETRY
The domain of definition of the function for realvalued is
(b) (c) (d)
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31 36968 JEE Mains Super40 Revision Series TRIGONOMETRY
If then is equal to (a)
3− 1x − πx − = 0π
2
2 cos − 1 x = cot − 1( )?2x − 1
2x√1 − x2( − 1, 1) − {0} ( − 1, 0)
( − 1, 1)
tan− 1( ) − cot − 1( )isx cos θ
1 − x sin θ
cos θ
x − sin θ2θ θ
θ
2θ
f(x) = √sin− 1(2x) +π
6x
[ − , ]1
4
1
2[ − , ]
1
2
1
2( − , )
1
2
1
9[ − , ]
1
4
1
4
u = cot − 1 √tanα − tan− 1 √tanα, tan( − )π
4
u
2√tanα
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(b) (c) (d)
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32 44201
JEE Mains Super40 Revision Series TRIGONOMETRY
The number of real solutions of is a.
b. one c. two d. infinite
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33 44373
JEE Mains Super40 Revision Series TRIGONOMETRY
The number of distinct real roots of in the interval
is (a) (b) (c) (d)
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34 45899
JEE Mains Super40 Revision Series TRIGONOMETRY
If then is equal to
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35 50042
JEE Mains Super40 Revision Series TRIGONOMETRY
If then the differencebetween the maximum and minimum values of is given by : (a) (b)
(c) (d)
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√cosα tanα cotα
tan− 1 √x(x + 1) + sin− 1 √x2 + x + 1 =π
2zero
∣∣ ∣∣
sinx cosx cosx
cosx sinx cosx
cosx cosx sinx
∣∣ ∣∣
= 0
− ≤ x ≤π
4
π
40 2 1 3
0 < x < 1, √1 + x2[{x cos(cot − 1 x) + sin(cot − 1 x)}2 − 1]12
u = √a2 cos2 θ + b2 sin2 θ + √a2 sin2 θ + b2 cos2 θ2,u2 (a − b)2
2√a2 + b2 (a + b)2 2(a2 + b2)
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36 61318
JEE Mains Super40 Revision Series TRIGONOMETRY
The general solution ofthe trigonometrical equation for is given by (a) (b) (c)
(d) non of these
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37 87428
JEE Mains Super40 Revision Series TRIGONOMETRY
If we consider only the principal values then the value inverse trigonometric functions
then the value of is (a) (b) (c) (d)
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38 1241998
JEE Mains Super40 Revision Series TRIGONOMETRY
If the sum of all the solutions of the equation
in is then k is equal to
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39 1269712
JEE Mains Super40 Revision Series TRIGONOMETRY
If then the value of can be (a) (b)
(c) (d)
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sinx + cosx = 1
n = 0, ± 1, ± 1 x = 2nπ x = 2nπ +π
2x = nπ + ( − 1)
n−
π
4
π
4
(cos − 1( ( − sin− 1) )1
5√2
4
√17
√29
3
29
3
√3
293
29
8 cosx. (cos( + x)cos( − x) − ) = 1π
6
π
6
1
2[0, π] kπ
θ = tan− 1(2 tan2 θ) − tan− 1( tan θ)1
3tan θ −2
12
32
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40 1408461
JEE Mains Super40 Revision Series TRIGONOMETRY
The value of for which is (a) (b) (c) (d)
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x sin(cot − 1(1 + x)) = cos(tan− 1 x)1
21 0
−1
2
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