Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry

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Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry

Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(C) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Q.1. Assertion: The value of sin600 cos300 + sin300 cos600 is 1
Reason: sin900=1 and cos900=0

Answer Answer: (b)

Q.2. Assertion: The value of 2tan2450+cos2300-sin2600 is 2.
Reason: value of tan450=1, cos300=√3/2 and sin600=√3/2.

Answer Answer: (a)

Q.3. Assertion: If x=2 sin2θ and y=2cos2θ+1 then the value of x+y=3.
Reason: For any value of θ, sin2θ+cos2θ=1

Answer Answer: (a)

Q.4. Assertion: sinA is the product of sin A.
Reason: The value of sinθ increases as θ increases.

Answer Answer: (d)

Q.5. Assertion: In a right ΔABC, right angled at B, if tanA=1, then 2sinA.cosA=1
Reason: cosecA is the abbreviation used for cosecant of angle A.

Answer Answer: (b)

Q.6. Assertion: In a right ΔABC, right angled at B, if tanA=12/5, then secA=13/5.
Reason: cotA is the product of cot and A.

Answer Answer: (c)

Q.7. Assertion: If xsin3θ+y cos3θ = sinθ cosθ and x sinθ = ycosθ, then x2+y2=1.
Reason: For any value of θ, sin2θ+cos2θ=1

Answer Answer: (a)

Q.8. Assertion: (cos4A-sin4A) is equal to 2cos2A-1.
Reason: The value of cosθ decreases as θ increases.

Answer Answer: (b)

Q.9. Assertion: If cosA+cos2A=1 then sin2A+sin4A=1.
Reason: sin2A+cos2A=1, for any value of A.

Answer Answer: (a)

Q.10. Assertion: sin(A+B)=sinA + sinB
Reason: For any value of θ, 1+tan2θ = sec2θ

Answer Answer: (d)

Frequently Asked Questions (FAQs)

What is trigonometry?

“Trigonometry” deals with the study of the relationship between the sides and angles of the right-angled triangle.

How many trigonometric functions are there?

There are 6 trigonometric functions. The three basic functions in trigonometry are sine, cosine and tangent. Based on these three functions the other three functions that are cotangent, secant and cosecant.

What is Sin θ?

sin θ = Perpendicular/Hypotenuse

What is Cosθ?

cos θ = Base/Hypotenuse

What is tanθ?

tan θ = Perpendicular/Base

What is cotθ?

cot θ = Base/Perpendicular

What is secθ?

sec θ = Hypotenuse/Base

What is cosecθ?

cosec θ = Hypotenuse/Perpendicular

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