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Question Number 6148 by saiful last updated on 16/Jun/16
if α,β andγ is corner in Δabc. indication that cos(β+γ)=−cosα
ifα,βandγiscornerinΔabc.indicationthatcos(β+γ)=−cosα
Answered by Rasheed Soomro last updated on 16/Jun/16
cos(β+γ)=−cosα −−−−−−−−−− ∵α,β,γ are angles of a triangle ∴ α+β+γ =180°⇒β+γ=180−α lhs:cos(β+γ)=cos(180−α) =cos 180 cos α + sin 180 sin α =(−1)cos α+(0)sin α=−cos α=rhs Proved
cos(β+γ)=−cosα−−−−−−−−−−∵α,β,γareanglesofatriangle∴α+β+γ=180°⇒β+γ=180−αlhs:cos(β+γ)=cos(180−α)=cos180cosα+sin180sinα=(−1)cosα+(0)sinα=−cosα=rhsProved

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