Inverse Trigonometric Functions MCQ Quiz - Objective Question with Answer for Inverse Trigonometric Functions - Download Free PDF
Last updated on Jun 15, 2025
Latest Inverse Trigonometric Functions MCQ Objective Questions
Inverse Trigonometric Functions Question 1:
Comprehension:
Consider the following for the two (02) items that follow:
Let
What is
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 1 Detailed Solution
Calculation:
Given,
The function is
The general derivative of
Apply the chain rule to find the derivative of y :
Hence, the correct answer is Option 3.
Inverse Trigonometric Functions Question 2:
Comprehension:
Consider the following for the two (02) items that follow:
Let
What is y equal to?
Answer (Detailed Solution Below)
3sin-1
Inverse Trigonometric Functions Question 2 Detailed Solution
Calculation:
Given,
The function is
We recognize that we can factor the expression as:
Thus, the function becomes:
Recognizing that this fits a known identity for inverse trigonometric functions:
Thus, we can simplify the expression to:
Hence, the correct answer is Option 4.
Inverse Trigonometric Functions Question 3:
If tan−1k+tan−1
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 3 Detailed Solution
Calculation:
Given,
Use the addition formula for inverse tangents:
Using this for
Since
Hence, the correct answer is Option 3.
Inverse Trigonometric Functions Question 4:
Find value of cot (tan-1 x + cot-1 x)
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 4 Detailed Solution
Concept:
tan-1 x + cot-1 x =
Calculation:
As we know tan-1 x + cot-1 x =
∴ cot (tan-1 x + cot-1 x) = cot
Inverse Trigonometric Functions Question 5:
is
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 5 Detailed Solution
Concept:
The maxima and minima of any function f(x) can be calculated by keeping it's first derivative as zero.
Now to find out whether it is a maxima or minima, we take it's double derivative now if the value is negative then it is a maxima and if it is positive it is a minima. For value equals to zero, it is unstable.
Solution: Given function,
To find out whether it is a maxima or minima, we take the double derivative.
Hence, 4>0. It is minima at x = 90°.
The correct answer is option 1.
Top Inverse Trigonometric Functions MCQ Objective Questions
If 4 tan-1 x + cot‑1 x = π, then x equals:
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 6 Detailed Solution
Download Solution PDFConcept:
Calculation:
4 tan-1 x + cot‑1 x = π
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 7 Detailed Solution
Download Solution PDFConcept:
Calculation:
S =
S =
S =
S =
S =
S =
S =
S =
The domain of sin-1 4x is:
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 8 Detailed Solution
Download Solution PDFConcept:
- The domain of a function f(x) is the set of values of x for which the function is defined.
- The value of sin θ always lies in the interval [-1, 1].
- sin-1 (sin θ) = θ.
- sin (sin-1 x) = x.
Calculation:
Let's say that sin-1 4x = θ.
⇒ sin (sin-1 4x) = sin θ
⇒ sin θ = 4x
Since, -1 ≤ sin θ ≤ 1
⇒ -1 ≤ 4x ≤ 1
⇒
⇒ x ∈
∴ The domain of the function is the closed interval
If sin-1 x + sin-1 y =
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 9 Detailed Solution
Download Solution PDFConcept:
sin-1 x + cos-1 x =
Calculation:
sin-1 x + sin-1 y =
⇒
⇒ π - ( cos-1 x + cos-1 y ) =
⇒ cos-1 x + cos-1 y =
The correct option is 2.
Find the value of
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 10 Detailed Solution
Download Solution PDFConcept:
Solution:
So, use the relation,
So,
If 3 sin-1 x + cos-1 x = π, then find the value of x?
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 11 Detailed Solution
Download Solution PDFConcept:
sin-1 x + cos-1 x = π/2, x ∈ [-1, 1]
Calculation:
Given: 3 sin-1 x + cos-1 x = π
⇒ 3 sin-1 x + cos-1 x = 2 sin-1 x + [sin-1 x + cos-1 x] = π
As we know that, sin-1 x + cos-1 x = π/2, x ∈ [-1, 1]
⇒ 2 sin-1 x + [π /2] = π
⇒ 2 sin-1 x = π - π/2
⇒ 2 sin-1 x = π/2
⇒ sin-1 x = π/4
⇒ x = sin π/4 = 1/√2
What is the principal solutions of the equation
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 12 Detailed Solution
Download Solution PDFConcept:
The principal solutions of a trigonometric equation are those solutions that lie between 0 and 2π.
Formula:
General solution of tan(x) = tan(α) is given as;
x = nπ + α where α ∈ (-π/2 , π/2) and n ∈ Z.
Calculation:
Given,
⇒ tan(x) = tan(-π/6)
∴ α = -π/6
⇒ x = nπ + (-π/6) , n ∈ Z
Putting n = 1 and 2, we get -
x = 5π/6 and 11π/6
What is the value of cos (2tan-1 x + 2cot-1 x) ?
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 13 Detailed Solution
Download Solution PDFConcept:
tan-1 x + cot-1 x =
Calculation:
To Find: Value of cos (2tan-1 x + 2cot-1 x)
cos (2tan-1 x + 2cot-1 x) = cos 2(tan-1 x + cot-1 x)
As we know, tan-1 x + cot-1 x =
cos (2tan-1 x + 2cot-1 x) = cos [2 ×
= cos π
= -1
In ΔABC, AB = 20 cm, BC = 21 cm and AC = 29 cm. What is the value of cot C + cosec C - 2tan A?
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 14 Detailed Solution
Download Solution PDFGiven:
AB = 20 cm
BC = 21 cm
AC = 29 cm
Concept used:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.
Calculation:
Using pythagoras theorem,
AC2 = AB2 + BC2
⇒ 292 = 202 + 212
ΔABC is a right angled triangle.
⇒ cot C = BC/AB = 21/20
⇒ cosec C = AC/AB = 29/20
⇒ tan A = BC/AB = 21/20
cot C + cosec C - 2tan A = 21/20 + 29/20 - 2 × 21/20
⇒ 8/20
⇒ 2/5
So, the value of cot C + cosec C - 2tan A = 2/5
Answer (Detailed Solution Below)
Inverse Trigonometric Functions Question 15 Detailed Solution
Download Solution PDFConcept:
Calculation:
Given,
⇒
⇒
⇒
⇒
⇒
⇒
This is true for all x ∈ R