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what is proof of 1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC

what is proof of 

1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC

 

Grade:10

2 Answers

Himanshu
103 Points
5 years ago
L.H.S. :  sin(A+B+C) = sin((A+B)+C)
=sin(A+B)cosC + cos(A+B)sinC
=[sinAcosB + cosAsinB]cosC + [cosAcosB – sinAsinB)sinC
=sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC
=R.H.S.
Hence. proved.
Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
5 years ago
Open up for sum of angles

Sin(A+B+C) sin(A+B)cosC + Cos(A+B)Sin C

and expand the below ones . you will get the answer

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