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sin(A+B+C)=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC prow that why

sin(A+B+C)=sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC  prow that
why
 

Grade:11

2 Answers

imran
55 Points
4 years ago
Hi SURAJ
let us
       given that sin(A+B+C)
that implise to sin(A+B)*cosC+cos(A+B)*sinC
then sinA*cosB*cosC+cosA*sinB*cosC+cosA*cosB*sinC-sinA*sinB*sinC
               therefore hence proved
        that simple thing that involved in this is sin(A+B)=sinA*cosB+cosA*sinB
                                                                                          and
                                                                          cos(A+B)=cosA*cosB-sinA*sinB
                                    kk THANK Q
Kushagra Madhukar
askIITians Faculty 629 Points
9 months ago
Dear student,
Please find the solution to your question.
 
Given that, LHS = sin(A+B+C) = sin({A+B} + c)
= sin(A+B)*cosC + cos(A+B)*sinC
= sinA*cosB*cosC + cosA*sinB*cosC + cosA*cosB*sinC – sinA*sinB*sinC
= RHS
Hence proved.
 
Hope it helps.
Thanks and regards,
Kushagra

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