Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Long Answer Questions: Introduction to Trigonometry

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q1: In the adjoining figure, ABCD is a rectanlge with breadth BC = 7 cm and ∠CAB = 30°. Find the length of side AB of the rectangle and length of diagonal AC. If the ∠CAB = 60°, then what is the size of the side AB of the rectangle. [Use √3 = 1.73 and √2 = 1.41, if required)
Class 10 Maths Chapter 8 Question Answers - Introduction to TrigonometryAns:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry 

Q2: Prove that:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q3: If x = r sin A cos C, y = r sin A sin C and z = r cos A, then prove that x2 + y2 + z2 = r2. 
Ans:
x = r sin A cos C; y = r sin A sin C; z = r cos A
Squaring and adding,
L.H.S. x2 + y2 + z2 = 2 sin2 A cos2C + r2 sin2 A sin2 C + r2 cos2 A
= r2 sin2 A(cos2 C + sin2 C) + r2 cos2 A
= r2 sin2 A + r2 cos2 A … [cos2θ + sin2θ = 1
= r2 (sin2 A + cos2 A) = r2 = R.H.S.

Q4: Prove that: (cot A + sec B)2 – (tan B – cosec A)2 = 2(cot A . sec B + tan B. cosec A)
Ans:
L.H.S.
= (cot A + sec B)2 – (tan B – cosec A)2
= cot2 A + sec2 B + 2 cot A sec B – (tan2 B + cosec2 A – 2 tan B cosec A)
= cot2 A + sec2 B + 2 cot A sec B – tan2 B – cosec2 A + 2 tan B cosec A
= (sec2 B – tan2 B) – (cosec2 A – cot2 A) + 2(cot A sec B + tan B cosec A)
= 1 – 1 + 2(cot A sec B + tan B cosec A) … [∵ sec2B – tan2 B = 1
cosec2A – cot2 A = 1
= 2(cot A . sec B + tan B . cosec A) = R.H.S.

Q5: Prove the following trigonometric identities: sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A.
Ans: 
L.H.S. = sin A (1 + tan A) + cos A (1 + cot A)
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q6: Prove the identity:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q7: Prove that: (1 + cot A + tan A). (sin A – cos A) = Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q8: Prove that:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q9: Find the value of:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry
Ans:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

Q10: Prove that: Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry = 2 cosec A
Ans:
Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry 

The document Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10
124 videos|457 docs|77 tests

Up next

FAQs on Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

1. What is trigonometry and why is it important in Class 10 mathematics?
Ans. Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is important in Class 10 mathematics as it helps in solving various real-life problems involving measurements, distances, heights, and angles.
2. How do we find the values of trigonometric ratios in Class 10?
Ans. In Class 10, we can find the values of trigonometric ratios using tables, calculators, or by using special triangles (like 30-60-90 and 45-45-90 triangles) to determine the ratios. We can also use the Pythagorean theorem and the definitions of sine, cosine, and tangent to find the values.
3. What are the basic trigonometric ratios and how are they used in Class 10?
Ans. The basic trigonometric ratios are sine, cosine, and tangent. In Class 10, these ratios are used to find the relationships between the angles and sides of a right triangle. For example, the sine ratio (sinθ) is defined as the ratio of the length of the side opposite the angle θ to the hypotenuse, cosine ratio (cosθ) is the ratio of the adjacent side to the hypotenuse, and tangent ratio (tanθ) is the ratio of the opposite side to the adjacent side.
4. How can trigonometry be applied in real-life situations?
Ans. Trigonometry can be applied in various real-life situations, such as measuring heights and distances, calculating the angles of elevation and depression, analyzing the motion of objects, designing structures, and solving navigation problems. It is also used in fields like engineering, physics, architecture, and astronomy.
5. What are the practical applications of trigonometry in Class 10 mathematics?
Ans. In Class 10 mathematics, trigonometry is used to solve problems related to heights and distances, angles of elevation and depression, and the concept of bearings. It helps in determining the heights of buildings or mountains, finding the distances between two points (without actually measuring them), and calculating the angles of inclination or depression.
124 videos|457 docs|77 tests
Download as PDF

Up next

Explore Courses for Class 10 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

ppt

,

Sample Paper

,

Free

,

Important questions

,

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

,

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

,

Objective type Questions

,

Extra Questions

,

Class 10 Maths Chapter 8 Question Answers - Introduction to Trigonometry

,

past year papers

,

study material

,

MCQs

,

pdf

,

video lectures

,

Summary

,

Semester Notes

,

Viva Questions

,

Exam

,

mock tests for examination

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

practice quizzes

;