Question
Fri December 28, 2012 By: R.k. Kumar

1.if a+b+c=180degrees,prove that sina + sinb + sinc=4cosa/2cosb/2cosc/2 2.Prove That sin8theta costheta - cos3theta sin6theta/cos2theta costheta - sin3thetasin4theta =tan2theta 3.Find perpendicular distance of the line joining the points(cos theta,sin theta)and (cos phy,sin phy)from the origin.

Expert Reply
Wed January 16, 2013
We would request you to please ask one question at a time. The solution to your first question is as follows:
 

sinA + sinB + sinC = 2sin[(A+B)/2]cos[(A-B)/2] + 2sinC/2cosC/2

                                  = 2sin[(?-C)/2]cos[(A-B)/2] + 2sinC/2cosC/2

                                  = 2cosC/2cos[(A-B)/2] + 2sinC/2cosC/2

                                  = 2cosC/2* [cos[(A-B)/2]+[cos(A+B)/2]          [Since, sinC/2 = cos(A+B)/2]

Now use cosC + cosD = 2 cos[(C+D)/2]cos[(C-D)/2]

                                  = 2cosC/2* [2cosA/2 cosB/2]

                                  = 4 cosA/2 cosB/2 cosC/2

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