Trigonometric Ratios of Complementary Angles Solutions for RS Aggarwal Class 10 Chapter 7
FAQs on RS Aggarwal Class 10 Solutions - Trigonometric Ratios of Complementary Angles
1. What is the correct method for solving problems in RS Aggarwal Class 10 Chapter 7 involving complementary angles?
The correct method involves a few key steps. First, identify pairs of angles in the expression that add up to 90°. Next, apply the appropriate complementary angle formula (e.g., sin(90° - A) = cos A, tan(90° - A) = cot A) to one of the angles in each pair. This converts the expression into a simpler form with common trigonometric ratios that can be cancelled or simplified to find the final answer.
2. How do I solve a problem like 'Evaluate sin 18° / cos 72°' from the RS Aggarwal textbook?
To solve this, you must follow the correct step-by-step process as per the CBSE guidelines:
- Recognise that 18° + 72° = 90°, so they are complementary angles.
- Choose one ratio to convert. For example, convert the sine ratio in the numerator using the formula sin A = cos(90° - A).
- Substitute A = 18°: sin 18° = cos(90° - 18°) = cos 72°.
- The expression becomes cos 72° / cos 72°.
- Simplify the fraction to get the final answer, which is 1.
3. What is the step-by-step solution for finding angle 'A' if sec 4A = cosec (A – 20°)?
To find the value of 'A' in such equations, the recommended method is:
- Use the complementary angle identity sec θ = cosec (90° - θ).
- Apply this to the left side of the equation: sec 4A = cosec (90° - 4A).
- Now the equation is cosec (90° - 4A) = cosec (A – 20°).
- Since the trigonometric ratios are the same, you can equate the angles: 90° - 4A = A – 20°.
- Solve the linear equation for A: 110° = 5A, which gives A = 22°.
4. Why is it important to pair up angles correctly when proving identities like tan 48° tan 23° tan 42° tan 67° = 1?
Pairing angles correctly is the most critical step because the entire solution depends on it. You must group angles that are complementary (add up to 90°). For this problem, the correct pairs are (48°, 42°) and (23°, 67°). Incorrect pairing will not allow you to use formulas like tan(90° - A) = cot A, which is needed to simplify the expression. Correct pairing allows tan 42° to become cot 48°, which cancels out with tan 48° (since tan θ × cot θ = 1).
5. What is the most common error students make when solving questions from this RS Aggarwal chapter?
A very common error is incorrectly applying the complementary formulas, for instance, writing sin(90° - A) as -cos A instead of cos A. Another frequent mistake is converting both angles in a complementary pair. For example, in sin 18° / cos 72°, converting both sin 18° to cos 72° and cos 72° to sin 18° leads back to the original problem. The correct approach is to convert only one of the ratios in a pair to match the other.
6. When should I use complementary angle formulas versus using standard angle values (like 0°, 30°, 45°)?
You should use complementary angle formulas when the angles given in the problem are non-standard (e.g., 18°, 48°, 72°) but appear in pairs that add up to 90°. Standard angle values are used only when the angles are explicitly 0°, 30°, 45°, 60°, or 90°. The purpose of complementary angle rules is specifically to solve problems where you do not know the exact trigonometric value of the given angles from memory.
7. How do the solutions for RS Aggarwal Class 10 Chapter 7 help master this topic for board exams?
The step-by-step solutions for RS Aggarwal Chapter 7 are designed to build a strong foundation. They demonstrate the precise application of formulas for different problem types, from simple evaluations to complex proofs. By following these methods, you learn how to structure your answers as per the latest 2025-26 CBSE pattern, which helps in scoring full marks in board exams. They clarify the logical flow required to solve any question involving complementary angles.
