If in a ΔABC,$$b(b+c)=a2$$ and $$c(c+a)=b2$$, then $$cos$$⁡A⋅$$cos$$⁡B⋅$$cos$$⁡$$C=$$

Question

If in a ΔABC,$$b(b+c)=a2$$ and $$c(c+a)=b2$$, then $$cos$$⁡A⋅$$cos$$⁡B⋅$$cos$$⁡$$C=$$

Infinity Learn · Accepted Answer

Given that $$b(b+c)=a2$$⇒$$bc=a2$$−$$b2sin$$⁡B⋅$$sin$$⁡$$C=sin2$$⁡A−$$sin2$$⁡Bsin⁡B⋅$$sin$$⁡$$C=$$$$sin$$⁡(A+B)$$sin$$⁡(A$$−$$B)$$sin$$ B · sinC  $$=$$ $$sin$$ C·$$sinA-B$$ $$sin$$⁡$$B=$$$$sin$$⁡(A$$−$$B)⇒$$2B=A$$ And  similarly $$c(c+a)=b2$$⇒$$2C=B$$ We have $$A+B+C=$$π  ⇒ $$2B$$ $$+B+$$ $$B2=$$π ⇒$$7B2=$$π⇒$$B=2$$$$π$$$$7$$⇒$$A=4$$$$π$$$$7$$, $$C=$$π$$7$$∴$$cos$$$$π$$$$7$$.$$cos2$$$$π$$$$7$$.$$cos4$$$$π$$$$7=$$$$sin$$ $$8$$$$π$$$$78$$ $$sin$$ π$$7=$$−$$18$$       $$cos$$ A $$cos$$ $$2A$$ $$cos$$ $$4A$$ .......$$cos$$ $$2n-1A=$$$$sin$$ $$2nA2nsinA$$

$If in a Δ A B C, b (b + c) = a^{2} and c (c + a) = b^{2}, then \cos A \cdot \cos B \cdot \cos C =$

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If in a ΔABC,b(b+c)=a2 and c(c+a)=b2, then cos⁡A⋅cos⁡B⋅cos⁡C=

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$If in a Δ A B C, b (b + c) = a^{2} and c (c + a) = b^{2}, then \cos A \cdot \cos B \cdot \cos C =$