Trigonometric ldentities and Equations Test

Result

Trigonometric ldentities and Equations Test - 9

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Question 1
4 / -1

If 5 cos 2θ + 2 cos² θ/2 + 1 = 0, where 0 < θ < π, then the value of θ

A
π/3 ± π

B
π/3 , cos^-1 (3/5)

C
cos^-1 (3/5) ± π

D
π/3 , π - cos^-1 (3/5)

Solution
Question 2
4 / -1

cos 2 χ + 7 = a (2 - sinχ) can have a real solution for

A
all values of a

B
a ϵ [2, 6]

C
a ϵ (-∞, 2)

D
a ϵ (0,∞)

Solution
Question 3
4 / -1

Number of solutions of |χ - 1| = cos χ is

A
2

B
3

C
4

D
None of the above

Solution
Question 4
4 / -1

The number of solutions of the equation sinχ cos 3χ = sin 3χ cos 5χ in [0, π/2] is

A
3

B
4

C
5

D
6

Solution
Question 5
4 / -1

If 1 + sin θ + sin² θ +... = 4 + 2√3; 0 < θ < π, θ ≠ π/2, then

A
θ = π/3

B
θ = π/6

C
θ = π/3 or π/6

D
θ = π/3 or 2π/3

Solution
Question 6
4 / -1

The most general solutions of the equation secχ - 1 = (√2 - 1) tan χ are given by

A
nπ + π/8

B
2nπ , 2nπ + π/4

C
2nπ

D
None of these

Solution
Question 7
4 / -1

The number of solutions of the equation sin 2χ + cos 4χ = 2 is

A
0

B
1

C
2

D
∞

Solution
Question 8
4 / -1

The solution of sinχ + sin 5χ = sin 3χ in (0, π/2) is

A

B

C

D

Solution
Question 9
4 / -1

If cot χ + cosec χ = √3 , then the principal value of (χ - π/6)

A
π/3

B
π/4

C
π/2

D
π/6

Solution
Question 10
4 / -1

The solution of equations cos² θ + sin θ + 1 = 0 lies in the interval

A

B

C

D

Solution