Maharashtra State BoardHSC Science (General) 11th
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Prove the following: If sin 2A = λsin 2B then prove that tan(A+B)tan(A-B)=λ+1λ-1 - Mathematics and Statistics

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Sum

Prove the following:

If sin 2A = λsin 2B then prove that `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`

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Solution

sin 2A = λsin 2B

∴ `(sin 2"A")/(sin 2"B") = lambda/1`

∴ `(sin2"A" + sin2"B")/(sin2"A" - sin2"B") = (lambda + 1)/(lambda - 1)`

∴ `(2sin((2"A" + 2"B")/2)*cos((2"A" - 2"B")/2))/(2cos ((2"A" + 2"B")/2)*sin((2"A" - 2"B")/2)) = (lambda + 1)/(lambda - 1)`

∴ `(sin("A" + "B")*cos("A" - "B"))/(cos("A" + "B")*sin("A" - "B")) = (lambda + 1)/(lambda - 1)`

∴ tan(A + B) · cot(A – B) = `(lambda + 1)/(lambda - 1)`

∴ `(tan("A" + "B"))/(tan("A" - "B")) = (lambda + 1)/(lambda - 1)`.

Concept: Trigonometric Functions of Sum and Difference of Angles
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 3 Trigonometry - 2
Miscellaneous Exercise 3 | Q II. (12) | Page 57
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