RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 7. Values of Trigonometric Functions at Sum of Difference of Angles

Subject: - Class 11th

Q. No. 26 of Exercise 7.1

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26

If sin(α + β) = 1 And sin(α – β) = 1/2, where , then find the values of tan(α + 2β) And tan(2α + β).

Given sin(α + β) = 1 And sin(α – β) = 1/2


⇒ α + β = 90° …(1) And α - β = 30° …(2)


Adding(1) And(2),


⇒ 2α = 120°


∴ α = 60°


Subtracting(2) from(1),


⇒ 2β = 60°


∴ β = 30°


Then,


∴ tan(α + 2β) = tan(60° + 2 × 30°) = tan 120° = -√3


And tan(2α + β) = tan(2 × 60° + 30°) = tan 150° = -(1/√3)


Chapter Exercises

Exercise 7.1
Exercise 7.2
Very Short Answer
MCQ

More Exercise Questions

1

If sinA = 4/5 And cosB = 5/13, where 0 <A, B < π/2, find the values of the following:

(i) sin(A +B)


(ii) cos(A +B)


(iii) sin(A –B)


(iv) cos(A -B)
2

If SinA = 12/13 And sinB = 4/5, where π/2<A < π And 0 <B < π/2, find the following:

(i) sin(A +B) (ii) cos(A +B)
2

If sinA = 3/5, cosB = –12/13, where A And B Both lie in second quadrant, find the value of sin(A +B).
3

If cosA = – 24/25 And cosB = 3/5, where π <A < 3π/2 And 3π/2 <B < 2π, find the following:

(i) sin(A +B) (ii) cos(A +B)
4

If tanA = 3/4, cosB = 9/41, where π<A < 3π/2 And 0 <B < π/2, find tan(A +B).
5

If sinA = 1/2, cosB = 12/13, where π/2<A < π And 3π/2 <B < 2π, find tan(A -B).
6

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7

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(iii) sin 360 cos 90 + cos 360 sin 90 (iv) cos 800 cos 200 + sin 800 sin 200
8

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(i) sin(A +B) (ii) cos(A +B) (iii) tan(A +B)
9

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10

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11

Prove that:

(i) (ii)


(ii)

12

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12

Prove that:
12

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13

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14

If tanA = 5/6 And tanB = 1/11, prove thatA +B = π/4.
14

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15

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cos2 π/4 - sin2
15

prove that:

sin2(n + 1)A – sin2nA = sin(2n + 1)A sinA
16

Prove that:
16

Prove that:
16

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16

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sin2B = sin2A + sin2(A-B) – 2sinA cosB sin(A-B)
16

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16

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17

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tan 8x – tan6x – tan 2x = tan 8x


tan 6x tan 2x
17

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17

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17

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Tan 9x tan 4x
18

Prove that:

19

If , show that .
20

If tanA = tanB, prove that .
21

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22

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23

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24

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25

If then prove that .
26

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27

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28

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29

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29

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29

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30

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31

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32

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33

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34

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