**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 sin60^{0} cos30^{0} + sin30^{0} cos60^{0} is 1 **Reason:** sin90^{0}=1 and cos90^{0}=0

## Answer

Answer: (b)**Q.2. Assertion: **The value of 2tan^{2}45^{0}+cos^{2}30^{0}-sin^{2}60^{0} is 2. **Reason:** value of tan45^{0}=1, cos30^{0}=√3/2 and sin60^{0}=√3/2.

## Answer

Answer: (a)**Q.3. Assertion:** If x=2 sin^{2}θ and y=2cos^{2}θ+1 then the value of x+y=3. **Reason: **For any value of θ, sin^{2}θ+cos^{2}θ=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 xsin^{3}θ+y cos^{3}θ = sinθ cosθ and x sinθ = ycosθ, then x^{2}+y^{2}=1. **Reason:** For any value of θ, sin^{2}θ+cos^{2}θ=1

## Answer

Answer: (a)**Q.8. Assertion:** (cos^{4}A-sin^{4}A) is equal to 2cos^{2}A-1. **Reason:** The value of cosθ decreases as θ increases.

## Answer

Answer: (b)**Q.9. Assertion:** If cosA+cos^{2}A=1 then sin^{2}A+sin^{4}A=1. **Reason: **sin^{2}A+cos^{2}A=1, for any value of A.

## Answer

Answer: (a)**Q.10. Assertion: **sin(A+B)=sinA + sinB **Reason:** For any value of θ, 1+tan^{2}θ = sec^{2}θ

## 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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