IfA+B+C=180°prove that sin(a+b/2 )=cos(c/2)

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asked Apr 16, 2021 194k views

3 votes

IfA+B+C=180°prove that sin(a+b/2 )=cos(c/2)

Mathematics
high-school

Joas asked

by Joas

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2 Answers

2 votes

Answer:

See Explanation

Explanation:

$A+B+C=180° \\ \\ A+B=180° -C \\ \\ dividing \: throughout \: by \: 2 \\ \\ (A+B)/(2)= (180° -C)/(2) \\ \\ (A+B)/(2)= (180 \degree)/(2) - (C)/(2) \\ \\ (A+B)/(2)= 90 \degree - (C)/(2) \\ \\ taking \: \sin \: ratio \: on \: both \: sides \\ \\ sin \bigg((A+B)/(2) \bigg)= \sin \bigg(90 \degree - (C)/(2) \bigg) \\ \\sin \bigg((A+B)/(2) \bigg)= \cos \bigg( (C)/(2) \bigg) \\ (\because \sin(90 \degree - \theta) = \cos \theta )\\ \\ thus \: proved$