In triangle PQR,find Sigma(q+r) cos P,if p, q | vedclass

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(C) We are given $\Sigma(q+r) \cos P = (q+r) \cos P + (r+p) \cos Q + (p+q) \cos R$.Expanding this,we get:$(q \cos P + r \cos P) + (r \cos Q + p \cos Q

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$2s$

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(C) We are given $\Sigma(q+r) \cos P = (q+r) \cos P + (r+p) \cos Q + (p+q) \cos R$.Expanding this,we get:$(q \cos P + r \cos P) + (r \cos Q + p \cos Q) + (p \cos R + q \cos R)$Rearranging the terms:$(q \cos P + p \cos Q) + (r \cos P + p \cos R) + (r \cos Q + q \cos R)$Using the projection law,we know that $r = q \cos P + p \cos Q$,$q = r \cos P + p \cos R$,and $p = r \cos Q + q \cos R$.Substituting these into the expression:$r + q + p = p + q + r$Since the semi-perimeter $s = \frac{p+q+r}{2}$,we have $p+q+r = 2s$.Therefore,$\Sigma(q+r) \cos P = 2s$.

In $\triangle PQR$,find $\Sigma(q+r) \cos P$,if $p, q, r$ denote its sides and $s = \frac{p+q+r}{2}$.

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