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Inverse Trigonometric Functions - 1 - JEE MCQ


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30 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Inverse Trigonometric Functions - 1

Inverse Trigonometric Functions - 1 for JEE 2025 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Inverse Trigonometric Functions - 1 questions and answers have been prepared according to the JEE exam syllabus.The Inverse Trigonometric Functions - 1 MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Inverse Trigonometric Functions - 1 below.
Solutions of Inverse Trigonometric Functions - 1 questions in English are available as part of our Mathematics (Maths) for JEE Main & Advanced for JEE & Inverse Trigonometric Functions - 1 solutions in Hindi for Mathematics (Maths) for JEE Main & Advanced course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Inverse Trigonometric Functions - 1 | 30 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) for JEE Main & Advanced for JEE Exam | Download free PDF with solutions
Inverse Trigonometric Functions - 1 - Question 1
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If ƒ(x) = √(2tan(x)),then f-1(√(2)) =

Detailed Solution for Inverse Trigonometric Functions - 1 - Question 1

Correct Answer :- b

Explanation :

Step 1: Write down the equation you need to solve
You want to find x such that
f(x) = √(2)
⟹ √(2 tan x) = √(2)

Step 2: Eliminate the square root
Square both sides (remembering (√A)2 = A):
(√(2 tan x))2 = (√(2))2
⟹ 2 tan x = 2

Step 3: Solve for tan x
Divide both sides by 2:
tan x = 2 / 2 = 1

Step 4: Find x from tan x = 1
On the principal branch (–π/2 < x < π/2), tan x = 1 gives
x = tan-1(1) = π/4

Step 5: State the inverse value
Therefore
f⁻¹(√(2)) = π/4

Inverse Trigonometric Functions - 1 - Question 2
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The value of cos15º− sin15º is

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Inverse Trigonometric Functions - 1 - Question 3
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The maximum value of sin x + cos x is

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Inverse Trigonometric Functions - 1 - Question 4
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The value of tan150 + cot150 is
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The value of tan150 + cot 150 

Inverse Trigonometric Functions - 1 - Question 5
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The number of solutions of the equation sin-1 x - cos-1 x = sin-1(1/2) is
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Hence , the given equation has only one solution.

Inverse Trigonometric Functions - 1 - Question 6
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What is the maximum and minimum value of sin x +cos x?
Detailed Solution for Inverse Trigonometric Functions - 1 - Question 6

Let y= sin x + cos x

dy/dx=cos x- sin x

For maximum or minimum dy/dx=0

Setting cosx- sin x=0

We get cos x = sin x

x= π/4, 5π/4———-

Whether these correspond to maximum or minimum, can be found from the sign of second derivative.

d^2y/dx^2=-sin x - cos x=-1/√2–1/√2 (for x=π/4) which is negative. Hence x=π/4 corresponds to maximum.For x=5π/4

d^2y/dx^2=-(-1/√2)-(-1/√2)=2/√2 a positive quantity. Hence 5π/4 corresponds to minimum

Maximum value of the function

y= sin π/4 + cos π/4= 2/√2=√2

Minimum value is

Sin(5π/4)+cos (5π/4)=-2/√2=-√2

Inverse Trigonometric Functions - 1 - Question 7
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Inverse Trigonometric Functions - 1 - Question 8
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Inverse Trigonometric Functions - 1 - Question 9
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Inverse Trigonometric Functions - 1 - Question 10
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Inverse Trigonometric Functions - 1 - Question 11
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Inverse Trigonometric Functions - 1 - Question 12
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Inverse Trigonometric Functions - 1 - Question 13
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*Multiple options can be correct
Inverse Trigonometric Functions - 1 - Question 14
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Inverse Trigonometric Functions - 1 - Question 15
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Equation of the image of the line x + y = sin–1(a3 + 1) + cos–1(a2 + 1) – tan–1(a + 1), a ∈ R about y-axis is given by-
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a = 0


Inverse Trigonometric Functions - 1 - Question 16
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Number of solutions of the equation 2 cot–12 + cos–1(3/5) = cosec–1 x is
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Inverse Trigonometric Functions - 1 - Question 17
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*Multiple options can be correct
Inverse Trigonometric Functions - 1 - Question 18
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Inverse Trigonometric Functions - 1 - Question 19
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Which one of the following can best represent the graph of the function, f (x) = cos–1(2x2 – 1)?
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Inverse Trigonometric Functions - 1 - Question 20
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Inverse Trigonometric Functions - 1 - Question 21
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Inverse Trigonometric Functions - 1 - Question 22
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Inverse Trigonometric Functions - 1 - Question 23
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Inverse Trigonometric Functions - 1 - Question 26
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The set of values of x, satisfying the equation tan2(sin–1x) > 1 is
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Inverse Trigonometric Functions - 1 - Question 27
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Inverse Trigonometric Functions - 1 - Question 28
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Inverse Trigonometric Functions - 1 - Question 29
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Inverse Trigonometric Functions - 1 - Question 30
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cos−1[cos(2cot−1(√2−1)] is equal to
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