Question

In A ABC, the tangent of half the difference of two angles is one-third
the tangent of half the sum of the angles. Then, the ratio of the sides
opposite to the angles is
(A) 2:1
(B) 1:3 (C) 1:5
(D) 1:4​

Answer 1

Answer:

option (A) is the correct answer

Step-by-step explanation:

Let A,B and C be the angles of a triangle. 

Let a,b and c be the opposite sides of these angles respectively.

According to the question,

tan[21(A−B)]=31tan[21(A+B)]

According to Napiers Anology, we can write the above equation as

a+ba−bcot2C=31tan[90−2C]

a+ba−bcot2C=31cot2C

Cancelling cot2C from the equation, weget

a+ba−b=31

3a−3b=a+b

2a=4b

a=2b

a:b=2:1

Hence, option (A) is the correct answer

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