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RD Sharma Class 10 Math Some Applications of Trigonometry Solutions - Free PDF Download

Last updated date: 24th May 2024
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Free PDF download of RD Sharma Solutions for Class 10 Maths Chapter 12 - Some Applications of Trigonometry

Free PDF download of RD Sharma Solutions for Class 10 Maths Chapter 12 - Some Applications of Trigonometry solved by Expert Mathematics Teachers on All Chapter 12 - Some Applications of Trigonometry Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks. Register for online coaching for JEE (Mains & Advanced), NEET, Engineering and Medical entrance exams.

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Class 10 Maths Chapter 12 RD Sharma Solutions - Some Applications of Trigonometry

Trigonometry is a branch of mathematics that deals with the lengths and angles of triangles. In simple words, it is the study of relationships between the angles, lengths and heights of triangles. The angles can be measured in degrees or in radians. As chapter 12 of R.D. Sharma class 10 maths, this branch of mathematics is concerned with specific functions of angles and their application to calculations. Since the chapter is very tricky, students have to be very observant while learning and applying the formulae in solving complex questions. Here we study the application of trigonometric functions in determining the height of buildings as well as in other fields like oceanography, criminology, electrical engineering, etc.

All the formulae used in trigonometry revolve around the three sides of a right-angled triangle: The base (B), the perpendicular (P) and the hypotenuse (H). When we apply the Pythagoras theorem, the equation that forms is: P2+B2=H2

The trigonometric ratios based on this theorem are sine, cosine, tangent, secant, cosecant and cotangent. The formula is as follows:

  • sin= P/H

  • cos= B/H

  • tan= P/B (sin A/cosA)

  • sec=H/B (1/cos A)

  • cosec=H/P (1/ sin A)

  • cot=B/P (cos A/ sin A)

The three main trigonometric identities to be kept in mind are:

  • sin2A+cos2A= 1

  • tan2A+1= sec2A

  • cot2A+1= cosec2A

We also have trigonometric sign functions. Here, ‘(𝛳)’ is a variable to denote a measured angle.They are:𝛳

  • Sin(-𝛳)= -sin𝛳

  • Cos(-𝛳)=cos𝛳

  • Tan(-𝛳)=-tan𝛳

  • Cot(-𝛳)=-cot𝛳

  • sec(-𝛳)=sec𝛳

  • cosec(-𝛳)=-cosec𝛳

FAQs on RD Sharma Class 10 Math Some Applications of Trigonometry Solutions - Free PDF Download

1. How important is Trigonometry for the class 10 Maths Board Exam?

Because of the complex and tricky formula, students tend to skip this chapter despite its importance while pursuing Engineering, Astronomy and Physics. This chapter cannot be cleared without practicing the formula regularly since there are so many to remember at once. When students begin their preparation, they should first make a chart of important formulas and keep it visible in their study for reference and to help learn it. At least four to five questions from this chapter are asked every year in the board exams hence Trigonometry has to be practiced regularly.

2. How do we calculate the sum and the differences of two angles?

As stated above, Trigonometry has three important trigonometric ratios which are the most important parts of this chapter: sin, cos and tan. All the trigonometric identities are formed based on these three ratios. So to derive the sum and difference of two angles, let us assume that there are two angles, A and B. The following will be the equations formed:

  • Sin (A+B)= sinAcosB+ cosAsinB

  • Sin (A-B)= sinAcosB- cosAsinB

  • Cos (A+B)= cosAcosB-sinAsinB

  • Cos (A-B)= cosAcosB+sinAsinB

  • Tan (A+B)=(tan A+tan B)/(1-tanAtanB)

  • Tan (A-B)=(tan A-tan B)/(1+tanAtanB)

3. What are double and triple angle identities in Trigonometry?

A double angle formula is a trigonometric identity which expresses a trigonometric function of 2𝛳 and triple angle formula expresses trigonometric function of 3𝛳. These are special cases of compound angle formulas. The formula for both the double angle and triple angle identities are given below as:

  1. For double angle:

  • sin2A = 2sinA cosA = [ 2 tan A + (1+tan2A)]

  • cos2A = cos2A–sin2A = 1–2sin2A = 2cos2A–1= [(1-tan2A)/(1+tan2A)]

  • tan 2A = (2 tan A)/(1-tan2A)

  1.  For triple angle:

  •     sin3A = 3sinA-4sin3A

  •     cos3A = 4cos3A-3cosA

  •     tan3A = [3tanA-tan3A]/[1-3tan2A]

4. How are the applications of Trigonometry as suggested in R. D. Sharma?

Trigonometry has several applications mainly in the field of engineering, aviation, criminology, astronomy, architecture, oceanography and game development. They are even used in music where the wave patterns in the form of sine and cosine can be used to develop music on the computer. In this chapter, the major discussion revolves around measuring the height of a building or a mountain. The trigonometric functions used here are calculated by the distance of the building from a viewpoint and the elevation angle. 

5. Are the questions on application of Trigonometry difficult?

If a student has great grip on his knowledge of the trigonometric identities, formulas and functions, this chapter will seem like a piece of cake. This is because, in this chapter, the basic trigonometric functions have been used to calculate height, length and distance of objects. In case of confusion, go through the examples for help. Try to solve those, then move ahead with the easy questions and as the foundation becomes stronger, climb the ladder and solve the complex ones. Students must practice strengthening their understanding of Trigonometry. Students download free study material from Vedantu site and app