RD Sharma Solutions Class 10 Maths Chapter 6 Exercise 6.2 Trigonometric Identities

Here, we've provided the RD Sharma Solutions for Class 10 Maths Chapter 6, Exercise 6.2 on Trigonometric Identities in a downloadable PDF format. This exercise focuses on simplifying expressions using fundamental trigonometric identities, essential for building a strong foundation in trigonometry. The solutions are designed to help students understand each step clearly, making it easier to solve similar problems independently. Access the PDF below for a detailed walkthrough.

RD Sharma Solutions Class 10 Maths Chapter 6 Exercise 6.2 PDF

RD Sharma Solutions Class 10 Maths Chapter 6 Exercise 6.2 Trigonometric Identities

Below is the RD Sharma Solutions Class 10 Maths Chapter 6 Exercise 6.2 Trigonometric Identities -

1. If cos θ = 4/5, find all other trigonometric ratios of angle θ.

Solution:

We have, cos θ = 4/5 And we know that, sin θ = √(1 – cos ² θ) ⇒ sin θ = √(1 – (4/5) ² ) = √(1 – (16/25)) = √[(25 – 16)/25] = √(9/25) = 3/5 ∴ sin θ = 3/5 Since, cosec θ = 1/ sin θ = 1/ (3/5) ⇒ cosec θ = 5/3 And, sec θ = 1/ cos θ = 1/ (4/5) ⇒ cosec θ = 5/4 Now, tan θ = sin θ/ cos θ = (3/5)/ (4/5) ⇒ tan θ = 3/4 And, cot θ = 1/ tan θ = 1/ (3/4) ⇒ cot θ = 4/3

2. If sin θ = 1/√2, find all other trigonometric ratios of angle θ.

Solution:

We have, sin θ = 1/√2 And we know that, cos θ = √(1 – sin ² θ) ⇒ cos θ = √(1 – (1/√2) ² ) = √(1 – (1/2)) = √[(2 – 1)/2] = √(1/2) = 1/√2 ∴ cos θ = 1/√2 Since, cosec θ = 1/ sin θ = 1/ (1/√2) ⇒ cosec θ = √2 And, sec θ = 1/ cos θ = 1/ (1/√2) ⇒ sec θ = √2 Now, tan θ = sin θ/ cos θ = (1/√2)/ (1/√2) ⇒ tan θ = 1 And, cot θ = 1/ tan θ = 1/ (1) ⇒ cot θ = 1

3.

Solution:

Given, tan θ = 1/√2 By using sec ² θ − tan ² θ = 1,

4.

Solution:

Given, tan θ = 3/4 By using sec ² θ − tan ² θ = 1,

sec θ = 5/4

Since, sec θ = 1/ cos θ ⇒ cos θ = 1/ sec θ = 1/ (5/4) = 4/5

So,

5.

Solution:

Given, tan θ = 12/5 Since, cot θ = 1/ tan θ = 1/ (12/5) = 5/12 Now, by using cosec ² θ − cot ² θ = 1 cosec θ = √(1 + cot ² θ) = √(1 + (5/12) ² ) = √(1 + 25/144) = √(169/ 25) ⇒ cosec θ = 13/5 Now, we know that sin θ = 1/ cosec θ = 1/ (13/5) ⇒ sin θ = 5/13 Putting value of sin θ in the expression we have, = 25/ 1 = 25

6.

Solution:

Given,

cot θ = 1/√3 Using cosec ² θ − cot ² θ = 1, we can find cosec θ cosec θ = √(1 + cot ² θ) = √(1 + (1/√3) ² ) = √(1 + (1/3)) = √((3 + 1)/3) = √(4/3) ⇒ cosec θ = 2/√3 So, sin θ = 1/ cosec θ = 1/ (2/√3) ⇒ sin θ = √3/2 And, we know that cos θ = √(1 – sin ² θ) = √(1 – (√3/2) ² ) = √(1 – (3/4))

= √((4 – 3)/4)

= √(1/4) ⇒ cos θ = 1/2 Now, using cos θ and sin θ in the expression, we have = 3/5

7.

Solution:

Given, cosec A = √2 Using cosec ² A − cot ² A = 1, we find cot A = 4/2 = 2

Benefits of Solving RD Sharma Solutions Class 10 Maths Chapter 6 Exercise 6.2

Solving RD Sharma's solutions for Class 10 Maths, Chapter 6, Exercise 6.2 on Trigonometric Identities provides several benefits for students preparing for their exams. Here’s why working through these exercises is advantageous:

Understanding Fundamentals : Trigonometric identities are a foundational topic in math, essential for understanding advanced concepts in trigonometry and calculus. This exercise helps reinforce the basics, building a solid foundation for future math courses.

Enhances Problem-Solving Skills : Trigonometric identities involve complex manipulations and transformations. By practicing these exercises, students develop skills in identifying and applying appropriate identities to simplify expressions, enhancing their analytical and problem-solving abilities.

Increases Speed and Accuracy : Regular practice with RD Sharma's exercises helps improve speed and accuracy, which is crucial for performing well in timed exams. Repeated exposure to similar types of problems trains students to solve them more quickly and accurately.

Prepares for Board Exams : Chapter 6 covers essential identities commonly tested in board exams. Solving these exercises thoroughly ensures students are well-prepared and confident to tackle similar questions in exams.

Builds Confidence : Mastering trigonometric identities can be challenging, but successfully solving these exercises builds students' confidence and encourages a positive attitude toward tackling difficult math topics.