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Question Number 70052 by ahmadshahhimat775@gmail.com last updated on 30/Sep/19

  sin A+sin B=n         and        cos A+cos B=m  sin (A+B)=?

sinA+sinB=nandcosA+cosB=msin(A+B)=?

Answered by $@ty@m123 last updated on 30/Sep/19

sin A+sin B=n  ⇒2sin ((A+B)/2)cos ((A−B)/2)=n ....(1)  cos A+cos B=m  ⇒2cos ((A+B)/2)cos ((A−B)/2) =m ...(2)  Dividing (1) by (2), we get  tan ((A+B)/2)=(n/m)  We have,  sin (A+B)=((2tan ((A+B)/2))/(1+tan^2 ((A+B)/2)))  =(((2n)/m)/(1+(n^2 /m^2 )))   =  ((2mn)/(m^2 +n^2 ))

sinA+sinB=n2sinA+B2cosAB2=n....(1)cosA+cosB=m2cosA+B2cosAB2=m...(2)Dividing(1)by(2),wegettanA+B2=nmWehave,sin(A+B)=2tanA+B21+tan2A+B2=2nm1+n2m2=2mnm2+n2

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