JEE Questions for Maths Trigonometric Ldentities And Equations Quiz 5 - MCQExams.com

If log_cosχ tanχ + log_sinχ cot χ = 0, then the most general solution χ is

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2 nπ - 3π/4, n ϵ Z
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2 nπ + π/4, n ϵ Z
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nπ + π/4, n ϵ Z
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None of these

The number of real solutions of the equations χ³ + χ² + 4χ + 2 sinχ = 0 in 0 ≤ χ ≤ 2π is

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four
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two
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one
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0

Number of solutions of the equation tanχ + secχ = 2 cos χ, χ ϵ [0, π] is

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0
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1
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2
0%
3

The positive integer value of n > 3 satisfying the equation
Maths-Trigonometric ldentities and Equations-54493.png

Maths-Trigonometric ldentities and Equations-54493.png

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8
0%
6
0%
5
0%
7

If sin θ = 1/2 and tan θ = 1/√3, ∀ n ϵ I , the most general value of θ is

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2nπ + π/6, ∀ n ϵ I
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2nπ + π/4, ∀ n ϵ I
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2nπ + π/3, ∀ n ϵ I
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2nπ + π/5, ∀ n ϵ I

The number of solutions of 2 sin χ + cos χ = 3 is

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1
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2
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infinite
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no solution

The solution of trigonometric equation cos⁴ χ + sin⁴ χ = 2 cos (2χ + π) cos (2χ - π) is

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0%
2)
0%
0%

The solution of the equation [sin χ + cos χ]^{1+sin 2χ} = 2 - π ≤ χ ≤ π is

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π/2
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π
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π/4
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3π/4
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π/3

Maths-Trigonometric ldentities and Equations-54503.png

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0%
2)
0%
0%

The general value of θ satisfying the equation 2 sin² θ - 3 sin θ - 2 = 0 is

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0%
2)
0%
0%

If 3 cosχ ≠ 2 sinχ, then the general solution of sin² χ - cos 2χ - sin 2χ is

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0%
2)
0%
0%

The most general values of θ satisfying tan θ + tan (3π/4 + θ) = 2 are given by

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0%
2)
0%
0%

The root of the equation 1 - cos θ = sin θ . sin θ/2 is

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0%
2)
0%
0%
None of these

The most general solution of √3 cos θ + sin θ = √2 is

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0%
2)
0%
0%

The general solution of |sinχ|= cos χ is (when n ϵ I) given by

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nπ + π/4
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2nπ ± π/4
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nπ ± π/4
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nπ -π/4

If sin θ = sin 15^o + sin 45^o, where 0^o < θ < 90^o, then θ is equal to

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45o
0%
54o
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60o
0%
72o
0%
75o

Maths-Trigonometric ldentities and Equations-54535.png

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α + β = 0
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α + β = 2n
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α + β = 2n + 1
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α + β = 2(2n + 1), for all n is an integer

The equation √3 sinχ + cos χ = 4 has

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infinitely may solutions
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no solution
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two solution
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only one solution

The most general value of θ satisfying the equations sin θ = sin α and cos θ - cos α is

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2nπ + α
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2nπ - α
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nπ + α
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2nπ - α

If 2sin² θ + √3 cos θ + 1 = 0, then the value of θ is

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π/6
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2π/3
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5π/6
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π

The solution of the equation 4 sin² χ + cos² χ = 1 is

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χ = 2nπ
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χ = nπ + 1
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χ = (n +π
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None of these

The number of values of χ in [0, 2π] satisfying the equation 3 cos 2χ - 10 cos χ + 7 = 0 is

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1
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2
0%
3
0%
4

{ χ ϵ R : cos 2χ + 2 cos² χ = 2} is equal to

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0%
2)
0%
0%

If cos χ ≠ - (1/, then solutions of cos χ + cos 2χ + cos 3χ = 0 are

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0%
2)
0%
0%

The number of solutions of sin χ = sin 2χ between -(π/and π/2 is

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3
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2
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1
0%
0

The number of solutions of the pair of equations 2 sin² θ - cos 2θ = 0 and 2 cos² θ - 3 sin θ = 0 in the interval [0, 2π] is

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0
0%
1
0%
2
0%
4

The number of solutions of the equation 1 + sin χ sin² χ/2 = 0, in [-π, π] is

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0
0%
1
0%
2
0%
3

Number of solutions of y = e^χ and y = sin χ is

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0
0%
1
0%
2
0%
infinite

If sin 3θ = sin θ, how many solutions exists such that 0 < θ < 2π ?

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8
0%
9
0%
5
0%
7

The equations 3 sin² χ + 10 cos χ - 6 = 0 is satisfied, if

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0%
2)
0%
0%

The general value of θ is the equation cos θ = 1/√2, tanθ = - 1 is

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0%
2)
0%
0%

The solution of tan 2θ tan θ = 1 is

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π/3
0%
(6n ± 1)π/6
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(4n ± 1)π/6
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(2n ± π)π/6

The set of values of θ satisfying the equation 2sin² θ - 5 sin θ + 2 > 0, where 0 < θ < 2π is

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0%
2)
0%
0%
None of these

The number of values of χ in the interval [0, 3π] satisfying the equation 2 sin² χ + 5 sinχ - 3 = 0 is

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6
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1
0%
2
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4

The general solution of sinχ - cos χ = √2, for any integer n is

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nπ
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2nπ + 3π/4
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2nπ
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(2n + 1)π

Which one of the following equations has no solution ?

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cosec θ - sec θ - cosec θ . sec θ
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cosec θ . sec θ = 1
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cos θ + sin θ = √2
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√3 sin θ - cos θ = 2

If tan (k + 1)θ = tan θ, then θ belongs to the set

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{nπ : n ϵ I}
0%
{nπ/2 : n ϵ I}
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{nπ/k : n ϵ I}
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{nπ/2k : n ϵ I}

Maths-Trigonometric ldentities and Equations-54576.png

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A.P.
0%
G.P.
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H.P.
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None of these

Maths-Trigonometric ldentities and Equations-54578.png

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0%
2)
0%
0%
None of these.

Let A and B denote the statements
A : cos α + cos β + cos γ = 0
B : sin α + sin β + sin γ = 0
If cos ( β - γ) + cos ( γ - α ) + cos (α - β ) = -(3/2), then

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A is correct and B is incorrect
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A is incorrect and B is correct
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both A and B are correct
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both A and B are incorrect

If cosec A + sec A = cosec B + sec B, then tan A tan B is equal to

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0%
2)
0%
0%

Maths-Trigonometric ldentities and Equations-54589.png

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0%
2)
0%
0%

Maths-Trigonometric ldentities and Equations-54595.png

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> 1
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≤ 1
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= 2
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None of these

Maths-Trigonometric ldentities and Equations-54597.png

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0%
2)
0%
0%

Maths-Trigonometric ldentities and Equations-54603.png

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0%
2)
0%
0%

Maths-Trigonometric ldentities and Equations-54609.png

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–1 and 1
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0 and 1
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1 and 2
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None of these

Maths-Trigonometric ldentities and Equations-54611.png

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0%
2)
0%
0%

Maths-Trigonometric ldentities and Equations-54617.png

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0%
2)
0%
0%
None of these

Maths-Trigonometric ldentities and Equations-54622.png

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1
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–1
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0
0%
None of these

Maths-Trigonometric ldentities and Equations-54624.png

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1
0%
2)
0%
0
0%
None of these

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