RD Sharma Solutions Class 11 Maths Chapter 9 – Trigonometric Ratios Of Multiple And Sub Multiple Angles (Updated For 2023-24)

RD Sharma Solutions Class 11 Maths Chapter 9 Trigonometric Ratios Of Multiple And Sub Multiple Angles: Looking for some quality helping guide that can assist you in understanding the Class 11 Maths syllabus? Well, you are standing in the right place. RD Sharma Solutions Class 11 Maths Chapter 9 Trigonometric Ratios Of Multiple And Sub Multiple Angles is what you need to prepare the Trigonometric Ratios with ease.

Download RD Sharma Solutions Class 11 Maths Chapter 9 PDF

RD Sharma Solutions Class 11 Maths Chapter 9

Exercise-wise: RD Sharma Solutions Class 11 Maths Chapter 9 PDF

RD Sharma Class 11 Solutions Exercise 9.1

RD Sharma Class 11 Solutions Exercise 9.2

RD Sharma Class 11 Solutions Exercise 9.3

Access RD Sharma Solutions Class 11 Maths Chapter 9

1. √[(1 – cos 2x) / (1 + cos 2x)] = tan x

Solution:

Let us consider LHS:

√[(1 – cos 2x) / (1 + cos 2x)]

We know that cos 2x = 1 – 2 sin² x

= 2 cos² x – 1

So,

√[(1 – cos 2x) / (1 + cos 2x)] = √[(1 – (1 – 2sin² x)) / (1 + (2cos²x – 1))]

= √[(1 – 1 + 2sin² x) / (1 + 2cos² x – 1)]

= √[2 sin² x / 2 cos² x]

= sin x/cos x

= tan x

= RHS

Hence proved.

2. sin 2x / (1 – cos 2x) = cot x

Solution:

Let us consider LHS:

sin 2x / (1 – cos 2x)

We know that cos 2x = 1 – 2 sin² x

Sin 2x = 2 sin x cos x

So,

sin 2x / (1 – cos 2x) = (2 sin x cos x) / (1 – (1 – 2sin² x))

= (2 sin x cos x) / (1 – 1 + 2sin² x)]

= [2 sin x cos x / 2 sin² x]

= cos x/sin x

= cot x

= RHS

Hence proved.

3. sin 2x / (1 + cos 2x) = tan x

Solution:

Let us consider LHS:

sin 2x / (1 + cos 2x)

We know that cos 2x = 1 – 2 sin² x

= 2 cos² x – 1

Sin 2x = 2 sin x cos x

So,

sin 2x / (1 + cos 2x) = [2 sin x cos x / (1 + (2cos²x – 1))]

= [2 sin x cos x / (1 + 2cos² x – 1)]

= [2 sin x cos x / 2 cos² x]

= sin x/cos x

= tan x

= RHS

Hence proved.

Important Topics of RD Sharma Class 11 Maths Chapter 9

The RD Sharma Solution is prepared in the most subtle way that enables students to learn the chapter in their most convenient manner. However, peeping at the important topics helps one get to the point before actually learning what is there in the chapter. So, here we are with the important topics the chapter includes-

• Values of trigonometric functions at ‘2x’ in terms of values at ‘x’.
  • Values of trigonometric functions at ‘x’ in terms of values at ‘x/2’.
  • Values of trigonometric functions at ‘x/2’ in terms of values at ‘cos x’.
• Values of trigonometric functions at ‘3x’ in terms of values at ‘x’.
• Values of trigonometric functions at ‘x’ in terms of values at ‘x/3’.
• Values of trigonometric functions at some important points

Access Other Important Chapters of RD Sharma Solutions Class 11 Maths

• Chapter 1 – Sets
• Chapter 2 – Relations
• Chapter 3 – Functions
• Chapter 4 – Measurement of Angles
• Chapter 5 – Trigonometric Functions
• Chapter 6 – Graphs of Trigonometric Functions
• Chapter 7 – Trigonometric Ratios of Compound Angles
• Chapter 8 – Transformation Formulae

Well, this is all that you need to chalk down your CBSE Class 11 maths exam strategy for  Trigonometric Ratios Of Multiple And Sub Multiple Angles. Have yourself RD Sharma Solutions Class 11 Maths Chapter 9 to help yourself with your mathematics exam preparation. 

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