Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions Chapter-5. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-5(a), Exe-5(b), Exe-5(c), Exe-5(d) with Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-5 Compound and Multiple Angles of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

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-: Select Topics :- 

Exe-5(a)

Exe-5(b)

Exe-5(c)

Exe-5(d)

Chapter Test

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Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

 Compound Angles

The algebraic sum of 2 or more angles can be called a compound angle. Trigonometric identities are used to represent compound angles. The basic operations of finding the sum and difference of functions can be computed using the concept of compound angles.

Trigonometric Ratios of Compound Angles

The formulae for trigonometric ratios of compound angles are as follows:

• sin (A + B) = sin A cos B + cos A sin B
• sin (A – B) = sin A cos B – cos A sin B
• cos (A + B) = cos A cos B – sin A cos B
• cos (A – B) = cos A cos B + sin A cos B
• tan (A + B) = [tan A + tanB] / [1 – tan A tan B]
• tan (A – B) = [tan A – tan B] / [1 + tan A tan B]
• sin (A + B) sin (A – B) = sin² A – sin² B = cos² B – cos² A
• cos (A + B) cos (A – B) = cos² A – sin² A – sin² B = cos² B – sin² A

Transformation of Products into Sum or Difference of Sines and Cosines:

(a) 2 sin A cos B = sin (A+B) + sin (A-B)

(b) 2 cos A cos B = cos (A+B) + cos (A-B)

(c) 2 cos A sin B = sin (A+B) – sin (A-B)

(d) 2 sin A sin B = cos (A-B) – cos (A+B)

Multiple and sub multiple Angles

(a) sin 2A = 2 sin A cos A = 2 tan A/(1+tan²A)

(b) cos 2A = cos2A – sin2A  = 2cos2A-1 = 1-2 sin2A

(c) tan 2A = 2 tan A/(1-tan²A)

(d) sin 3A = 3 sinA – 4 sin3A

(e) cos 3A = 4 cos3A – 3 cos A

(f) tan 3A = (3 tan A- tan³A)/(1-tan²A)

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Exe-5(a)

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Some part of the Questions is given for hint , see question from your text book :

Question 1-

Compute :

(i) sin 15⁰ from the function of 60⁰ and 45⁰

(ii) cos 345⁰ from the function of 60⁰ and 45⁰

(iii) tan 105⁰ from the function of 60⁰ and 60⁰

(iv) sin 135⁰ from the function of 180⁰ and 45⁰

(v) cos 195⁰ from the function of 150⁰ and 45⁰

(vi) cosec (13 π/12)

Question 2-

………………………

………………………..

……………………….

Question 31-

If A + B = 225⁰, prove that tan A + tan B = 1- tan A tan B

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Exe-5(b)

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 5-11 to 5-12

Question 1-

Convert the following products into sum or difference. If angle  are given in degree evaluate from table 

(i) 2 sin 48⁰ cos 12⁰

 

Question 2-

………………

( see question from your text book 🙂

………………….

Question 22-

What is the value of cos 10 + sin 20/ cos 20 – sin 10?

 

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Exe-5(c)

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 5-25 to 5-26

Question 1-

Evaluate:

(i) 2 sin 15 cos 15 

(ii) ………..

(iii)………..

Question 2-

( see question from your text book :)……………………..

……………………….

……………………..

Question 17-

Calculate without using table tan 20 tan 40 tan 80.

 

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 Exe-5(d)

Compound and Multiple Angles S.Chand ISC Class-11 Maths Solutions

Page 5-27 to 5-29

Question 1-

(i) (sin∅ – cos ∅)² = 1 – sin 2∅

(ii) {cos (θ/2) + sin(θ/2)}² = 1 + sin θ

Question 2-

( see question from your text book :)………………………

……………………..

……………………….

Question 45-

If tan …………………

 

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Chapter Test

Compound and Multiple Angles OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 5-33 to 5-3

Question 1-

Show that tan  ………………….. 4 sin 60.

Question 2-

( see question from your text book :)…………………….

………………………..

Question 16-

Prove that cos …………………. x-1.

…………………………..

………………………….

Question 21- 

If tan …………………………….

 

 

-: End of Compound and Multiple Angles Solution :-

Return to :-  OP Malhotra S. Chand ISC Class-11 Maths Solutions

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