= 4 ^2 1 + 4 ^2 , = 4 ^2 1 + 4 ^2 , = 4 ^2 1 + 4 ^2 where

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

sin⁡β=4sin⁡2α1+4sin⁡2α,sin⁡γ=4sin⁡2β1+4sin⁡2β,sin⁡α=4sin⁡2γ1+4sin⁡2γ\sin \beta = \frac{4 \sin^2 \alpha}{1 + 4 \sin^2 \alpha}, \sin \gamma = \frac{4 \sin^2 \beta}{1 + 4 \sin^2 \beta}, \sin \alpha = \frac{4 \sin^2 \gamma}{1 + 4 \sin^2 \gamma} where α,β,γ∈R\alpha, \beta, \gamma \in \mathbb{R}, then the maximum value of (sin⁡α+sin⁡β+sin⁡γ)2(cos⁡α+cos⁡β+cos⁡γ)2\frac{(\sin \alpha + \sin \beta + \sin \gamma)^2}{(\cos \alpha + \cos \beta + \cos \gamma)^2} is ?

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