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# RD Sharma Solutions for Class 11 Maths Chapter 9: Trigonometric Ratios of Multiple and Sub Multiple Angles

The ninth chapter in the textbook RD Sharma is based on the double and half angles. The chapter also includes the formula for handling triple and (1/3)rd angles. The chapter teaches the students about the formulae that are used to simplify the equations or expressions given. Chapter 9 – Values of Trigonometric Functions at Multiples and Submultiples of an Angle contains various questions in the exercises, and the RD Sharma Solutions provided by the Aakash solution offers answers to the questions in each exercise.

The questions given in the chapter are “required to prove” type and the concepts covered in this chapter include trigonometric equation values of 'x' are expressed in terms of 'x/2' values, values of 'x/2' are expressed in terms of values of ‘x'.

• sin A = 2 sin (A/2) cos(A/2)
• sin A = (2 tan(A/2))/(1+tan2(A/2))
• cos A = cos2(A/2) – sin2 (A/2)
• cos  A = 2 cos2 (A/2) - 1
• cos A = 1 - 2 sin2 (A/2)
• 1 + cos A = 2 cos2 (A/2)
• 1 - cos A = 2 sin2 (A/2)
• cos A = (1−tan2(A/2))/(1+tan2(A/2))
• tan2 (A/2) = (1−cosA)/(1+cosA)
• tan A = (2tan(A/2))/(1−tan2(A/2))

The chapter also includes the values of trigonometric functions at '3x' that are expressed in terms of 'x' values. Values of trigonometric functions at 'x' are expressed in terms of 'x/3' values.

• sin A = 3 sin (A/3) - 4 sin3 (A/3)
• cos A = 4 cos3 (A/3) - 3 cos (A/3)

The last topic includes the trigonometric function values at a critical point. The RD Sharma solutions have many solved examples and diagrams that offer step-by-step definitions of various complex topics and numerous practice questions. The definition of formulae representing the values of trigonometric functions at multiples and submultiples of 'X' is introduced in this chapter. Since this chapter involves important transformations thus, these formulae are very important to remember, and the students need to practise these thoroughly to grasp these concepts fully. RD Sharma Solutions are fully exam-oriented and designed to help students succeed in their board exams. They would be able to conveniently succeed in their final exam if they practice these questions.

• For a better understanding of the solutions, each step is clearly explained.
• The Aakash Institute is devoted to helping students understand their homework and prepare for exams. Therefore, we have provided answers for all the questions from RD Sharma's Class 11th Maths textbook.
• Students will be able to revise the syllabus during their exams in a shorter amount of time and earn excellent marks.

## Key features of Aakash institute RD Sharma solutions for class 11th Maths Chapter 9- Trigonometric Ratios of Multiple and Sub Multiple Angles

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