Question

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

Answer 1

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`

Answer 2

Explanation: