Discussion

Question:

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

sin(α + β + γ) = $\frac{1}{\sqrt{2}}$ , cosec(β + γ - α) = $\frac{2}{\sqrt{3}}$ and tan(γ + α - β) = $\frac{1}{\sqrt{3}}$

What are the values of α, β, γ?

Explanation:

We evaluate options:

Option (1) Let α = 37.5, β = 52.5, γ = 45.

∴ α + β – γ = 45

∴ sin (α + β – γ) = $\frac{1}{\sqrt{2}}$

β + γ – α = 60

cosec(β + γ – α) = $\frac{2}{\sqrt{3}}$

γ + α – β = 30

tan(γ + α – β) = $\frac{1}{\sqrt{3}}$

Hence, option (a).

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