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Question Number 20646 by oyshi last updated on 30/Aug/17

i f \cos (β - γ) + \cos (γ - α) + \cos (α - β) = - \frac{3}{2}

s o p r o o f i t,

Σ \cos α = 0, Σ \sin α = 0

Answered by $@ty@m last updated on 31/Aug/17

G i v e n,

\cos (β - γ) + \cos (γ - α) + \cos (α - β) = - \frac{3}{2}

\Rightarrow 2 \cos (β - γ) + 2 \cos (γ - α) + 2 \cos (α - β) = - 3

\Rightarrow Σ (2 c o s β c o s γ + 2 s i n β s i n γ) + 3 = 0

\Rightarrow Σ (2 c o s β c o s γ + 2 s i n β s i n γ) + Σ ({s i n}^{2} α + {c o s}^{2} α) = 0

\Rightarrow {Σ {c o s}^{2} α + Σ 2 c o s β c o s γ} + {Σ {s i n}^{2} α + Σ 2 s i n β s i n γ} = 0

\Rightarrow {(Σ \cos α)}^{2} + {(Σ \sin α)}^{2} = 0

\Rightarrow Σ \cos α = 0, Σ \sin α = 0

Commented by ajfour last updated on 31/Aug/17

t h a n k s i m m e n s e l y .

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