Assertion and Reason Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry
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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:
(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)Related Posts
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Frequently Asked Questions (FAQs)
“Trigonometry” deals with the study of the relationship between the sides and angles of the right-angled triangle.
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.
sin θ = Perpendicular/Hypotenuse
cos θ = Base/Hypotenuse
tan θ = Perpendicular/Base
cot θ = Base/Perpendicular
sec θ = Hypotenuse/Base
cosec θ = Hypotenuse/Perpendicular
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