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

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)

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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)

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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)

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

Answer

Answer: (d)

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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)

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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)

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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)

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

Answer

Answer: (b)

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

Answer

Answer: (a)

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

Answer

Answer: (d)

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