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JEE Exam  >  JEE Tests  >  Mathematics (Maths) Class 12  >  Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - JEE MCQ

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - JEE MCQ


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5 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions below.
Solutions of Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions questions in English are available as part of our Mathematics (Maths) Class 12 for JEE & Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions solutions in Hindi for Mathematics (Maths) Class 12 course. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free. Attempt Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions | 5 questions in 10 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mathematics (Maths) Class 12 for JEE Exam | Download free PDF with solutions
Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 1
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): sin-1(sin(2π/3)) = 2π/3

Reason (R): sin -1(sin θ) = θ, if q ∈ [(-π)/2, π/2]

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 1
The principal value branch of sin–1x is [(-π)/2, π/2]

Let x = sin θ ⇒ θ = sin–1x

sin–1(sin θ) = sin–1 x = θ

sin–1(sin θ) = θ, if θ ∈ [(-π)/2, π/2]

Hence R is true.

Hence A is false.

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 2
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Principal value of cos–1(1) is π

Reason (R): Value of cos 0° is 1

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 2
In case of Assertion

cos-1(1) = y

Cos y= 1

Cos y = cos 00 [∴ cos 00 = 1]

∴ y = 0

⇒ Principal value of cos–1 (1) is 0

Hence Assertion is in correct.

Reason is correct.

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Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 3
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Range of tan–1x is [(-π/2, π/2)]

Reason (R): Domain of tan–1x is R.

Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 3

Domain of tan x is the set {x : x ∈ R and x ≠ (2n + 1) π/2, n ∈ Z} and Range is R.

⇒ tan x is not defined for odd multiples of π/2.

If we restrict the domain of tangent function to [(-π)/2, π/2], then it is one-one and onto with its range as R. Actually tan x restricted to any of the intervals etc., is bijective and its range is R.

Thus tan–1x can be defined as a function whose domain is R and range could be any of the intervals and soon.

∴ Both A and R are true but R is not correct explanation of A.

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 4
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): Range of cot–1 x is (0, π)
Reason (R): Domain of tan–1 x is R.
Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 4

Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 5
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Directions : In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.

Assertion (A): Principal value of sin-1(1/√2) is π/4

Reason (R): Principal value of cot-1(-1/√3) is π/3
Detailed Solution for Test: Inverse Trigonometric Functions- Assertion & Reason Type Questions - Question 5
sin-1(1/√2) = sin-1(sin (π/4))

= π/4

cot-1((-1/√3) = y

Cot y = -1/√3

= -cot(π/3)

= -cot (π - (π/3)

= cot(2π/3)

⇒ cot-1(-1/√3) = 2π/3

Hence Assertion is correct and Reason is incorrect.

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