Inverse Trigonometric Functions Test

Result

Inverse Trigonometric Functions Test - 4

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Question 1
1 / -0.25

If ƒ(x) = √(2tan(x)),then f^-1 (√(2)) =

A
0

B
1

C
√(2)

D
2

Solution

Correct Answer :- b
Explanation : ƒ(x) = √(2tan(x))
x = √(2tan(x))
x² = (2tan(x))
(x² )/2 = tan(x)
tan^-1 (x^2)/2 = x
By putting x = √2, we get
x = 1
Question 2
1 / -0.25

The value of cos15^º −sin15^º is

A

B

C
0

D

Solution
Question 3
1 / -0.25

If 2tan⁻¹ (cos x) = tan⁻¹ (2cosec x) , then x =

A
π/6

B
π/4

C
π/3

D
None of these.

Solution

If 2 tan^-1 (cos x) = tan ^-1 (2 cosec x),
2tan^-1 (cos x) = tan^-1 (2 cosec x)
= tan^-1 (2 cosec x)
= cot x cosec x = cosec x = x = π/4
Question 4
1 / -0.25

tan⁻¹ (−2) + tan⁻¹ (−3) is equal to

A
π/4

B
3 π/4

C
5 π/4

D

Solution

tan^-1 (-2) + tan^-1 (-3)
Question 5
1 / -0.25

The values of x which satisfy the trigonometric equation are :

A
±1/2

B
±√2

C
±2.

D
±

Solution
Question 6
1 / -0.25

The maximum value of sin x + cos x is

A
1

B
2

C
√2

D

Solution
Question 7
1 / -0.25

The value of tan15⁰ + cot15⁰ is

A
2 √3

B
4

C
√3

D
Not defined.

Solution

The value of tan15⁰ + cot 15⁰
Question 8
1 / -0.25

is equal to

A

B

C

D
None of these

Solution
Question 9
1 / -0.25

The number of solutions of the equation sin^-1 x - cos^-1 x = sin^-1 (1/2) is

A
3

B
1

C
2

D
Infinite.

Solution

Hence , the given equation has only one solution.
Question 10
1 / -0.25

A
1

B
-1

C
0

D
None of these

Solution

cot^-1 a - cot^-1 b + cot^-1 b - cot^-1 c - cot^-1 a = 0