Question #bfbd7

1 Answer
P dilip_k
Jan 31, 2018

#tan(a+b) =3tana #

#=>tan(a+b)/tana =3#

#=>(sin(a+b)cosa)/(sinacos(a+b)) =3#

By componendo and dividendo we get

#=>(sin(a+b)cosa+sinacos(a+b)) /(sin(a+b)cosa-sinacos(a+b))=(3+1)/(3-1)#

#=>sin(a+b+a) /sin(a+b-a)=4/2#

#=>(2sin(2a+b)cosb)/(2sinbcosb)=2#

#=>(sin(2a+2b)+sin2a)/(sin2b)=2#

#=>sin(2a+2b)+sin2a=2sin2b#

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