Can you prove that?

Question

#sin(S-A)sin(S-B)+ sin(S-C)sin(S)= sinA*sinB if A+B+C=2S#

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Answer 1 · 2018-07-15T04:50:50

Please see below

Things to know:-#2sinAsinB=cos(A-B)-cos(A+B) and cos(-A)=cosA#

#LHS=sin(S-A)sin(S-B)+sin(S-C)sinS#

#=1/2[2sin(S-A)sin(S-B)+2sin(S-C)sinS]#

#=1/2[cos(cancel(S)-Acancel(-S)+B)-cos(S-A+S-B)+cos(cancel(S)-Ccancel(-S))-cos(S-C+S)]#

#=1/2[cos(B-A)-cos(2S-A-B)+cos(-C)-cos(2S-C)]#

#=1/2[cos(B-A)-cos(cancel(A)cancel(+B)+Ccancel(-A)cancel(-B))+cosC-cos(A+Bcancel(+C)cancel(-C))]#

#=1/2[cos(A-B)-cos(A+B)cancel(+cosC)cancel(-cosC)]#

#=1/2[2sinAsinB]=sinAsinB=RHS#