Question

for any triangle ABC prove that

Answer 1

hope it helps you. gud luck

Answer 2

Step-by-step explanation:

$\sf LHS\:=\: \dfrac{k\,sin\,A\:+\:k\,sin\,B}{k\,sin\,C}\:=\: \dfrac{sin\,A+sin\,B}{C}$

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$\sf \quad=\: \dfrac{2sin\left(\dfrac{A+B}{2}\right)cos \left(\dfrac{A-B}{2}\right)}{2sin \dfrac{C}{2}\times \dfrac{C}{2}}$

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$\sf \quad=\: \dfrac{cos\left(\dfrac{A-B}{2}\right)}{sin\dfrac{C}{2}}$

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$\sf \because sin\left(\dfrac{A+B}{2}\right)\:=\:sin\left(\dfrac{\pi}{2}-\dfrac{C}{2}\right)$

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$\sf \quad=\:cos\dfrac{C}{2}$

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$\large{\underline{\sf{\blue{Hence\:Proved}}}}$