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)


26

Chapter Exercises

More Exercise Questions

6

If SinA = 1/2, cosB = , where π/2<A < π And 0 <B < π/2, find the following:

(i) tan(A +B)(ii) tan(A -B)