# RS Aggarwal Class 10 Chapter 12 Solutions (Trigonometric Ratios of Complementary Angles)

RS Aggarwal Class 10 Maths Solutions for Chapter 12 ‘Trigonometric Ratios of Complementary Angles’ are created by our subject matter experts to help you ace Class 10 board exams. The main topics in this chapter of RS Aggarwal Class 10 Maths Solutions include complementary angles and evaluation of the trigonometric ratios without using trigonometric tables. All your doubts in the chapter can now be easily resolved with the help of our exercise solutions.

Chapter 12 of RS Aggarwal Class 10 book has only 1 exercise that contains 15 questions. The way these 15 questions are organized it will become easy for you to revise the concepts of the chapter. The questions are based upon finding the value of trigonometric ratios using various identities. The easy step-by-step solutions of these RS Aggarwal’s problems will give you complete information about the concepts and you will be able to score well in your Class 10 board exams.

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## Important Topics of RS Aggarwal Class 10 Maths Solutions Chapter 12: Trigonometric Ratios of Complementary Angles

**Introduction of Complementary Angles**:

You may be familiar with that complementary angles are those sets of two angles whose sum is equal to 90°.

**For example- ** 20° and 70° are the complementary angles.

Thus, two angles P and Q are complementary angles if,

∠P + ∠Q = 90°

We can say that P complements to Q and vice versa.

If we talk about right-angle ∆ABC. We all know the measure of one angle is always fixed to 90° which tells us that the remaining two angles are always complementary angles because we know that the sum of angles in a triangle is always 180°.

In a right-angled triangle ABC. If A and C are considered as complementary angles.

We can conclude that:

⇒∠A + ∠C = 90°

For the given triangle, trigonometric ratios are of ∠A are as follows:

- Sin A = BC / AC
- Cosec A = AC / BC = 1 / Sin A
- Cos A = AB / AC
- Sec A = AC / AB =1 / Cos A
- Tan A = BC / AB
- Cot A = AB / BC = 1 / Tan A

Now, the trigonometric ratios of a complement of A i.e C are as follows:

As we know, ∠C = 90°- A the side opposite to the 90°- A is AB and adjacent to 90°- A is BC

- Sin C = Sin(90°- A ) = AB / AC
- Cos C = Cos(90°- A ) = BC / AC
- Tan C = Tan(90°- A ) = AB / BC
- Cosec C = Cosec(90°- A ) = BC / AB
- Sec C = Sec (90°- A ) = AC/ BC
- Cot C = Cot (90°- A ) = BC / AB

Comparing the above relations, it can be seen that:

- Sin (90°- A )= Cos A
- Cos (90°- A ) = Sin A
- Tan (90°- A ) = Cot A
- Sec(90°- A ) = Cosec A
- Cosec (90°- A ) = Sec A
- Cot (90°- A ) = Tan A

### Exercise Discussion of RS Aggarwal Class 10 Maths Solutions Chapter 12: Trigonometric Ratios of Complementary Angles

- Chapter 12 of RS Aggarwal Class 10 Maths Solutions has only one exercise which consists of a total of 15 questions. These questions are designed in such a way that covers all the important aspects of this chapter.
- The first 8 problems of RS Aggarwal Class 10 Maths Solutions of Chapter 12 are divided into two kinds of questions. The first one is of the evaluation type at which you need to find the value from the given trigonometric relations whereas in the second kind of question you need to prove the relations. All 8 questions use the concepts of complementary angles.
- The next 7 problems are quite tough to solve, as these questions are quite lengthy. The questions are generally of proof of the relation type. There are some questions also at which you need to give the answers in range lying between 0° and 45°.

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