If tan (A + B) = √3 and tan (A – B) = 1 and A, B (B < A) are acute angles, find the values of A and B.
Answer :
tan (A + B) = √3
So, tan (A + B) = tan 60° [Since, tan 60° = √3]
⇒ A + B = 60° …(i)
tan (A – B) = 1
tan (A – B) = tan 45° [tan 45° = 1]
⇒ A – B = 45° …(ii)
From equation (1) and (2), we get
A + B + A – B = 60° + 45°
⇒ 2A = 105o
⇒ A = 52½o
on substituting the value of A in equation (i), we get
52½o + B = 60°
⇒ B = 60° – 52½o = 7½o
Therefore, the value of A = 52½o and B = 7½o
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