# If a and B Are Acute Angles Such that Tan a =1/3, Tan B = 1/2 and Tan (A + B) = Show That A+B = 45^0 - Mathematics

If A and B are acute angles such that tan A =1/3, tan B = 1/2  and tan (A + B) = show that  A+B = 45^0

#### Solution

Given:

tan A = 1/3 and tan B = 1/2

tan (A+B) = (tan A + tan B)/(1- tan A  tan B)

On substituting these values in RHS of the expression, we get:

(tan A + tan B )/(1- tan A tan B) = ((1/3 +1/2))/((1-1/3xx1/3) =((5/6))/(1-1/6) = ((5/6))/((5/6))=1

⇒ tan (A + B) = 1= tan 45^0      [ ∵ tan 450 =1]

∴ A+B = 45

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 16
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