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Assertion & Reason Test: Introduction to Trigonometry - CAT MCQ


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14 Questions MCQ Test - Assertion & Reason Test: Introduction to Trigonometry

Assertion & Reason Test: Introduction to Trigonometry for CAT 2024 is part of CAT preparation. The Assertion & Reason Test: Introduction to Trigonometry questions and answers have been prepared according to the CAT exam syllabus.The Assertion & Reason Test: Introduction to Trigonometry MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Assertion & Reason Test: Introduction to Trigonometry below.
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Assertion & Reason Test: Introduction to Trigonometry - Question 1
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : The value of sin θ = 4/3 in not possible.

Reason : Hypotenuse is the largest side in any right angled triangle.

Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 1
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

Here, the perpendicular is greater than the hypotenuse which is not possible in any right triangle.

Assertion & Reason Test: Introduction to Trigonometry - Question 2
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion: The value of sec210o - cot280o is 1

Reason: The value of sin 30o = 1/2

Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 2
Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

We have,

sec2 10° - cot2 80° = sec2 10° - cot2(90° - 10°)

= sec2 10° — tan2 10° = 1

Also, sin30° = 1/2

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Assertion & Reason Test: Introduction to Trigonometry - Question 3
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : In a right angled triangle, if tanθ = 3/4, the greatest side of the triangle is 5 units.

Reason: (greatest side)2 = (hypotenuse)2 = (perpendicular)2 + (base) 2.

Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 3
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Greatest side =

units.

Assertion & Reason Test: Introduction to Trigonometry - Question 4
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : In a right angled triangle, if cosθ = 1/2 and sinθ = √3/2, then tanθ = √3

Reason: tanθ = sinθ/cosθ
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 4
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Assertion & Reason Test: Introduction to Trigonometry - 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): Cot A is the product of Cot and A.

Reason (R): The value of sinq increases as q increases.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 5
In case of assertion

cot A is not the product of cot and A. It is the cotangent of ∠A.

∴ Assertion is incorrect.

In case of reason:

The value of sin q increases as q increases in interval of θ°< θ° < 90°

∴ Reason is correct:

Hence, the assertion is incorrect but the reason is correct.

Assertion & Reason Test: Introduction to Trigonometry - Question 6
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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): If tan A = cot B, then the value of (A + B) is 90°.

Reason (R): If sec θ sin θ = 0, then the value of q is 0°.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 6
In case of assertion

tan A = cot B (Given)

tan A = tan(90° – B)

[∵ tan (90° - θ) = cot θ]

A = 90° – B

Hence, A + B = 90°.

∴ Assertion is correct.

In case of reason:

Given, sec θ.sin θ = 0

or,

or, tan θ = 0 = tan 0°

∴ θ = 0°

∴ Reason is correct:

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

Assertion & Reason Test: Introduction to Trigonometry - Question 7
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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): If k + 1 = sec2 θ (1 + sin θ) (1 – sin θ), then the value of k is 1.

Reason (R): If sin θ + cos θ = √3 then the value of tan θ + cot θ is 1.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 7
In case of assertion

k + 1 = sec2 θ(1 + sin θ)(1 – sin θ)

or, k + 1 = sec2 θ(1 – sin2 θ)

or, k + 1 = sec2 θ. cos2 θ

[∵ sin2 θ + cos2 θ = 1]

or,

or, k + 1 = 1

or, k = 1 – 1

∴ k = 0.

∴ Assertion is incorrect.

In case of reason:

Given sin θ + cos q = √3

Squaring on both sides,

(sin θ + cos θ)2 = (√3)2

sin2 θ + cos2 θ + 2 sin θ cos θ = 3

1 + 2 sin θ cos θ = 3

2 sin θ cos θ = 2

sin θ cos θ = 1 ... (i)

∴

∴ Reason is correct:

Hence, Assertion is incorrect but reason is correct.

Assertion & Reason Test: Introduction to Trigonometry - Question 8
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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): If sin A = √3/2, then the value of 2 cot2 A - 1 is -1/3.

Reason (R): If q be an acute angle and 5 cosec q = 7, then the value of sin θ + cos2 θ – 1 is 10.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 8
In case of assertion

∴ Assertion is correct.

In case of reason:

∴ Reason is incorrect:

Hence, assertion is correct but reason is incorrect.

Assertion & Reason Test: Introduction to Trigonometry - Question 9
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : sin2 67o + cos2 67o = 1

Reason : For any value of θ, sin2θ + cos2θ = 1
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 9
Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

sin2θ + cos2θ = 1

sin267o + cos267o = 1

Assertion & Reason Test: Introduction to Trigonometry - Question 10
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : sin 47° = cos 43°

Reason : sin θ = cos (90 + θ), where θ is an acute angle.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 10
Assertion (A) is true but reason (R) is false. Assertion is true, but reason is not correct.

sin θ = cos (90 - θ)

sin 47° = cos (90 — 47°) = cos43°

Assertion & Reason Test: Introduction to Trigonometry - Question 11
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : If cos A + cos2A = 1 then sin2A + sin4A = 2

Reason : 1 - sin2 A = cos2A, for any value of A.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 11
Assertion (A) is false but reason (R) is true.

cos A + cos2A = 1

cos A = 1 - cos2A = sin2A

sin2 A + sin4A = cos A + cos2 A = 1

sin2 A + sin4 A = 1

Assertion & Reason Test: Introduction to Trigonometry - Question 12
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Direction: In the Following Questions, A Statement of Assertion (A) Is Followed by A Statement of Reason (R). Mark The Correct Choice As:

Assertion : The value of sinθcos (90 — θ) + cos θsin (90 — 0) equals to 1.

Reason : tanθ = sec (90 — θ)
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 12
Assertion (A) is true but reason (R) is false.

sin θ • cos (90 — θ) + cos θ sin(90 — θ)

= sin θ • sin θ + cos θ • cos θ

= sin2 θ + cos2 θ = 1

and, tan θ = cot (90 — θ)

Assertion & Reason Test: Introduction to Trigonometry - Question 13
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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): The value of tan47γ/cot43γ is 1.

Reason (R): The value of the expression (sin 80° – cos 80°) is negative.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 13
In case of assertion

∴ Assertion is correct.

In case of reason:

80° is near to 90°, sin 90° = 1 and cos 90° = 0

So, the given expression sin 80° – cos 80° > 0

So, the value of the given expression is positive.

∴ Reason is incorrect:

Hence, the assertion is correct but the reason is incorrect.

Assertion & Reason Test: Introduction to Trigonometry - Question 14
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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): If x = 2 sin2 θ and y = 2 cos2 θ + 1 then the value of x + y = 3.

Reason (R): If tan α = 5/12, then the value of sec α is 13/12.
Detailed Solution for Assertion & Reason Test: Introduction to Trigonometry - Question 14
In case of assertion

We have x = 2 sin2 θ

and y = 2 cos2 θ + 1

Then, x + y = 2 sin2 θ + 2 cos2 θ + 1

= 2(sin2 θ + cos2 θ) + 1

= 2 × 1 + 1

[∵ sin2 θ + cos2 θ = 1]

= 2 + 1 = 3.

∴ Assertion is correct.

In case of reason:

tan α = 5/12

Using identity; sec2 α – tan2 α = 1

sec2 α = 1 + tan2 α

∴ Reason is correct:

Hence, both assertion and reason are correct but reason is not the correct explanation for assertion.

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