I have a question from trigonometric ratios chapter in which it is asked to find the value of angle A and B if tan (A – B) = 1/√3 and cos (A + B) = √3, 0° ≤ (A + B) ≤ 90° and A > B.
RS Aggarwal, Class 10, chapter 11, question no 25.
Rajan@2021Guru
If tan (A – B) = 1/√3 and cos (A + B) = √3, 0° ≤ (A + B) ≤ 90° and A > B, then find A and B
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Given
tan(A+B)=√3⟹A+B=60∘⋯(1)
tan(A−B)=1/√3
⟹A−B=30∘⋯(2)
(1) + (2)
⟹2A = 90∘
⟹A = 45∘
Put A value in (1)
⟹B = 60∘−45∘
=15∘