Class - 9 | Trigonometry | Solutions

Trigonometry is a chapter of Class 9 that most of the students must be learning in 9 for the first time in their entire life. Though it is their first time reading this chapter, they might have already seen the exercises and solutions of their seniors. They must have gone through the important t-ratios, t-formulae, and much more that one really needs to study before starting this chapter.

However, the solutions are not too easy if you lack practice. So, here's a solution guide for the Trigonometry unit for students of class 9, especially those residing in Nepal.

We have classified the solutions based on the chapter they are taught inside the unit 'Trigonometry'.

1. Trigonometric Identities

  1. 38 solved questions and answers of Trigonometry. Answer

Trigonometric Identities are the equations in Trigonometry that are always true for any values of the reference angle. Solving such questions requires a little knowledge and trick. You need to solve many questions related to it to be able to solve these questions very easily.


2. Trigonometric Values

  1. Evaluate sin135° and sin(-135°) without using a calculator. Answer
  2. Evaluate cosec(-1485°) without using a calculator. Answer
  3. Evaluate cos20° + cos40° +cos140° + cos160° Answer
  1. Find the value of: [ tan(180-Θ). cot(90-Θ). cos(360-Θ) ] [ sin(-Θ). tan(90+Θ). tan(180-Θ)] Answer
  1. If sinA = 12/13 , find cosA and tanA. Answer
  1. Prove that: cot Ï€/20 . Cot 3Ï€/20 .cot5Ï€/20 . Cot7Ï€/20 . Cot 9Ï€/20 = 1 Answer
  2. Prove that: cos^2 7Ï€/8 + cos^2 5Ï€/8 + cos^2 3Ï€/8 + cos^2 Ï€/8 = 2 Answer
  3. Prove that: cos Ï€/8 + cos 3Ï€/8 + cos 5Ï€/8  + cos 7Ï€/8 = 0 Answer
Trigonometric Values also referred to as Values of Trigonometric Ratios is the chapter where we have to use the values of standard angles of Trigonometry to solve or prove the given questions. You must know the values of all trigonometric ratios at standard angles and C.A.S.T. formula to be able to solve such questions.

3. Compound Angles

  1. Evaluate cot15 Answer
  2. Evaluate cos15 Answer
  3. Evaluate sin15 Answer
  4. Evaluate tan15 Answer
  1. Evaluate tan75 Answer
  1. Evaluate sin105 Answer
  2. Evaluate sin135 Answer
  3. Evaluate cosec(-1485) Answer
  1. If tanA= 5/6 and tanB = 1/11, prove that: A+B = 45°. Answer
  2. Prove that: tan²A -tan²B = {sin(A+B).sin(A-B)}/ cos²A.cos²B Answer
  3. If tan(a+b)=x and tan(a-b)=y find the values of tan2a and tan2b. Answer
Compound Angles are the angles that are formed by either addition or subtraction of standard angles and other angles. (Eg. :(45°-30° = 15°, or 45°-20°= 25°). There are separate formulae of cos, sin, tan, and cot as compound angles which you must know to solve these questions.


4. Derivations

  1. Derive cot(a-b) formula. Answer
In derivations, we derive the formula of compound angles.

5. Geometrical Proofs

  1. Prove geometrically, the value of sin30°, cos30°, and tan30°. Answer
  2. Prove geometrically, the value of sin45°, cos45°, and tan45°. Answer
In geometrical proofs, we derive the values of standard angles of trigonometric ratios using a right-angled triangle by the relation of their sides. This is the most important chapter not for examination but for solving real-life problems as well as to prove that you have understood Trigonometry.

Formula:

While solving the above exercises, you will definitely need to know these formulae which you can also access by visiting our blog about Compound Angles. You will know the derivation of all such formulae there.

General Identities

  1. sin²A + cos²A = 1
  2. cosec²A - cot²A = 1
  3. sec²A - tan²A = 1

Compound Angles Formula

  1. sin(A+B) = sinA.cosB + cosA.sinB
  2. sin(A-B) = sinA.cosB - cosA.sinB
  3. cos(A+B) = cosA.cosB - sinA.sinB
  4. cos(A-B) = cosA.cosB + sinA.sinB
  5. tan(A+B) = (tanA + tanB)/(1-tanAtanB)
  6. tan(A-B) = (tanA - tanB)/(1 +tanAtanB)
  7. cot(A+B) = (cotAcotB -1)/(cotB + cotA)
  8. cot(A-B) = (cotAcotB +1)/(cotB - cotA)

We hope that you have got the solutions for Trigonometry. We wish you all the best for class 9's examination. This blog is all about Science and Mathematics of Class 9 and Class 10. It will help you a lot with your studies. Whilst, you can check some of our recommended blogs:


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