# If Tan (A – B) = 1/Sqrt(3) and Tan (A + B) = Sqrt(3), 0^0 ≤ (A + B) ≤ 90^0 and a > B, Then Find a and B. - Mathematics

If tan (A – B) = 1/sqrt(3) and tan (A + B) = sqrt(3), 0^0 ≤ (A + B) ≤ 90^0 and A > B, then find A and B.

#### Solution

Here, tan (A – B) = 1/sqrt(3)
⇒ tan (A – B) = tan 30^0   [∵ tan 30^0 = 1/sqrt(3)]
⇒ (A – B) = 30^0           …….(i)
Also, tan (A + B) = sqrt(3)

⇒ tan (A + B) = tan 60^0 [            ∵ tan 60^0 =sqrt(3)]
⇒ A + B = 600                                       …….(ii)
Solving (i) and (ii), we get:
A = 450 and B = 15

Concept: Trigonometric Ratios and Its Reciprocal
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 6 T-Ratios of some particular angles
Exercises | Q 25
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