If each α,β and γ is a position acute angle such that \Sin(\alpha+\beta-\gamma)=1/\sqrt{2},\Cosec(\beta+\gamma-\alpha)=2/\sqrt3 and \tan(\gamma+\alpha-\beta)=1/\sqrt3 What are the values of α,β,γ ?

Correct Answer is : (37.5°, 52.5°, 45°)

Indian Institute of Foreign Trade 2010 Solved Paper

Question : 6 of 135

Marks: +1, -0

If each α,β and γ is a position acute angle such that

\Sin(α+β-γ)=1/√{2},\Cosec(β+γ-α)=2/√3

and

\tan(γ+α-β)=1/√3

What are the values of α,β,γ ?

Solution:

\Sin(α+β-γ)=1/√2

then

α+β-γ=45°

...(1)
If

\Cosec(β+γ-α)=2/√3

then

β+γ-α=60°

...(2)
if

\tan(γ+α-β)=1/√3

then

γ+α-β=30°

...(3)
Adding we get

α+β+γ=135°

...(4)
from 1,2,3 and 4 we get

α=37.5°

therefore answer is option 'A'

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