RS Aggarwal Solutions Class 10 Chapter 7 - Trigonometric Ratios of Complementary Angles (Ex 7A) Exercise 7.1 - Free PDF
FAQs on RS Aggarwal Solutions Class 10 Chapter 7 - Trigonometric Ratios of Complementary Angles (Ex 7A) Exercise 7.1 - Free PDF
1. How do I solve questions from RS Aggarwal Class 10 Maths, Exercise 7.1 on Complementary Angles?
The primary method for solving problems in this exercise is to use the complementary angle identities. First, look for pairs of angles within the trigonometric expression that add up to 90°. Next, convert one of the trigonometric ratios into the ratio of its complement (for instance, rewrite sin(A) as cos(90°-A)). This step is designed to simplify the expression, frequently leading to the cancellation of terms or the application of fundamental identities like sin²θ + cos²θ = 1.
2. What is the correct step-by-step method to evaluate an expression like cos 37° / sin 53° in Exercise 7.1?
To correctly evaluate this expression, follow these precise steps as per the CBSE pattern:
- Step 1: Identify the complementary pair. Observe that the sum of the angles is 37° + 53° = 90°.
- Step 2: Convert one of the ratios. It is best practice to convert only one part of the pair. Let's convert the numerator: cos 37° can be expressed as cos(90° - 53°).
- Step 3: Apply the relevant identity. Use the formula cos(90° - A) = sin A. This transforms cos(90° - 53°) into sin 53°.
- Step 4: Simplify the expression. Your expression now becomes sin 53° / sin 53°, which simplifies to 1.
3. Why is it necessary to convert only one of the trigonometric ratios in a pair like tan 10° / cot 80°?
It is crucial to convert only one ratio to create a common term for simplification. The entire goal is to make the numerator and denominator (or different parts of an expression) identical so they can be cancelled out. If you were to convert both—changing tan 10° to cot 80° and also changing cot 80° to tan 10°—you would end up with cot 80° / tan 10°, which is no simpler than the original problem. The strategy hinges on creating symmetry by altering only one component of the complementary pair.
4. What is a common mistake students make when solving 'Prove That' questions in this chapter?
A frequent error is to manipulate both the Left-Hand Side (LHS) and the Right-Hand Side (RHS) of the equation at the same time. The correct and standard approach, especially for board exams, is to start with the more complex side (usually the LHS) and apply a sequence of logical steps using complementary angle formulas and other algebraic identities. You must work on that one side until it is transformed to match the other side. Working on both sides can break the logical flow of the proof and may result in a loss of marks.
5. How does the identity sin²θ + cos²θ = 1 play a role in solving problems with complementary angles?
This fundamental Pythagorean identity often serves as the final step to simplify an expression. For example, you might encounter a problem like simplifying sin²20° + sin²70°. At first, this doesn't look like the identity. However, by using the complementary angle rule, you can convert sin²70° to cos²20° (since 70° + 20° = 90°). The expression then becomes sin²20° + cos²20°, which simplifies directly to 1. This demonstrates how complementary angle conversions and basic identities are used together to solve complex problems.
6. Where can I find accurate, step-by-step solutions for all questions in RS Aggarwal Class 10 Chapter 7, Exercise 7.1 for the 2025-26 session?
You can find comprehensive and reliable solutions for every problem in RS Aggarwal Class 10 Maths Chapter 7, Exercise 7.1, right here on Vedantu. Our solutions are meticulously crafted by subject matter experts to align with the latest CBSE guidelines for the 2025-26 academic year, ensuring you learn the correct, most efficient methods for scoring full marks.
7. What are the six essential trigonometric identities for complementary angles needed for this exercise?
To master every question in this exercise, you must be proficient with the following six identities:
- sin(90° – A) = cos A
- cos(90° – A) = sin A
- tan(90° – A) = cot A
- cot(90° – A) = tan A
- sec(90° – A) = cosec A
- cosec(90° – A) = sec A
These form the foundation for every simplification and proof in this chapter.
