Chapter 8 Introduction to Trigonometry Assertation & Reasoning Questions Class 10th

Direction: 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

1.) Assertion: The value of cosec 30°+cot45°is 3.

Reason: cosec 30°=2, cot 45°=1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

2.) Assertion: If    =45° then the value of cosec^2     is 2.

Reason: cosec ^2 45°=( 2 ^1/2) 2 =2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

3.) Assertion: if tanθ=cotθ then the value of secθ is 2^1/2.

Reason: tanθ=cotθ

tan^2θ=1 =tanθ=1

θ=45°

∴sec45°= 2^1/2

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

5.) Assertion: The value of sinA is always less than 1

Reason: SinA is the product of sin and A

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

6.) Assertion: 2 tan^245° + cos^230° – sin^260° is 2

Reason: The value of sin60°cos30° + sin30° cos60° is 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not  the correct explanation for Assertion.

7.) Assertion: cosecA is the abbreviation used for cosecant of angle A.

Reason: cotA is the product of cot and A.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

8.) Assertion: ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is 24/7

Reason: tan C = Opposite side/Adjacent side

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

9) Assertion:The value of tan 60°/cot 30° is equal to1.

Reason: tan 60° = √3 and cot 30° = √3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

10.) Assertion: 1 – cos^2A is equal to sin^2A.

Reason: sin^2A + cos^2A = 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

11.) Assertion: 2 tan 30°/(1 + tan^230°) =sin60°

Reason : tan 30° = 1/√3

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

12.) Assertion: sin 2A = 2 sin A is true when A =0°

Reason: sin 2A = sin 0° = 0

2 sin A = 2 sin 0° = 0

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

13.) Assertion: The maximum value of 1/cosecα is 1.

Reason: If cosec θ – cot θ = 13, the value of (cosec θ + cot θ) is 3.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

14.) Assertion: Reciprocal of sinθ is cosecθ

Reason: The value of sin θ  increases as θ  increases.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion.

15.) Assertion: cotA is not defined for A = 0°

Reason: sin θ=cos θ for all values of θ.

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason  are  false.

Ans: c) assertion  is true but reason  is  false.

16.) Assertion: If sin30° = 1/2 ,cos30°=(3^1/2)/2 then the value of tan30°is 1/(3)^1/2.

Reason: tan30°=sin30°/cos30°

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

17.) Assertion: In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals= 1

Reason: cosec A (sin B cos C + cos B sin C)

= cosec A × sin(B+C) = cosec A × sin(180 – A)

= cosec A × sin A = cosec A × 1/cosec A

= 1

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

18.) Assertion: If tan A = 1/2 and tan B = 1/3, then the value of A + B is π/4

Reason: tan(A + B) = (tan A + tan B)/(1 – tan A tan B)

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

19.) Assertion: The value of sin 50° – sin 70° + sin 10° is equal to 0.

Reason: sin(A – B) = sin A cos B – cos A sin B

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

20.) Assertion: The value of 4 × sin x × sin(x + π/3) × sin(x + 2π/3) is sin3x.

Reason: cos a + 2cos b + cos c = 2 then a, b, c are in 2b=a+c

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

21.) Assertion: The value of cos² 48° – sin²12° is √5 + 1/8.

Reason: If tan x = (cos 9 + sin 9)/(cos 9 – sin 9), then x =45

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: a.) Both Assertion and Reason are correct and Reason is  the correct explanation for Assertion.

22.) Assertion: In a triangle ABC, cosec A (sin B cos C + cos B sin C) equals 1.

Reason: If sin A = 3/4, then  cos A= √7/4and tan A= 3/√7

a.) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

b.) Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c.) assertion is true but the reason is false.

d.) both assertion and reason are false.

Ans: b.) Both Assertion and Reason are correct but Reason is not  the correct explanation for Assertion.

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

Answer: (b)

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

Answer: (a)