If each $$\alpha,\beta$$ and $$\gamma$$ is a positive acute angle such that $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}},Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ and $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$. What are the values of $$\alpha,\beta,\gamma$$?
if $$Sin(\alpha+\beta-\gamma)=\frac{1}{\sqrt{2}} $$then $$\alpha+\beta-\gamma$$ = 45° ...(1)
if $$Cosec(\beta+\gamma-\alpha)=\frac{2}{\sqrt{3}}$$ then $$\beta+\gamma-\alpha$$ = 60° ...(2)
if $$tan(\gamma+\alpha-\beta)=\frac{1}{\sqrt{3}}$$ then $$\gamma+\alpha-\beta$$ = 30° ...(3)
Adding we get $$\alpha+\beta+\gamma$$ = 135° ...(4)
from 1,2,3 and 4 we get $$\alpha$$ = 37.5° therefore answer is option 'A'
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