How do I prove that #2 sin ((C+D)/2) cos ((C-D)/2) = sin C+sin D#?
2 Answers
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)sin(A+B)=sinAcosB+cosAsinB#
#•color(white)(x)sin(A-B)=sinAcosB-cosAsinB#
#"Adding the 2 equations gives"#
#sin(A+B)+sin(A-B)=2sinAcosB#
#"Subtracting the 2 equations gives"#
#sin(A+B)-sin(A-B)=2cosAsinB#
#"let "C=A+B" and "D=A-B#
#rArrA=(C+D)/2" and "B=(C-D)/2#
#rArrsinC+sinD=2sin((C+D)/2)cos((C-D)/2)#
See the proof below
Explanation:
We need
Therefore,