Question

please solve this....​

Answer 1

Step-by-step explanation:

$\sf \: A ,\: B \: and \: C \: are \: the \: angles \: of \: a \: triangle \: \\ \\ so \: \: \: \: A + B + C = \pi \\ \therefore \:A + B = \pi - C \\\therefore \:B + C = \pi - A \\ \therefore \:C + A = \pi - B \\ \\ \\ \\L.H.S = \frac{sin(B + C) + sin(C + A) + sin(A + C)}{sin(\pi + A) + sin(3\pi + B) + sin(5\pi + C)} \\ \\ = \frac{sin( \pi - A) + sin(\pi - B) + sin(\pi - C)}{ - sinA - sinB - sinC} \\ \\ = \frac{ \: \: \cancel{(sinA + sinB + sinC)}}{ - \: \cancel{(sinA + sinB + sinC)}} \\ \\ = - 1 \\ \\ = R.H.S$