Given #3 TanA*TanB=1#,show that 2cos(A+B)=cos(A-B) ?

1 Answer
P dilip_k
Jun 12, 2017

Given

#3tanAtanB=1#

#=>1/(tanAtanB)=3#

#=>(cosAcosB)/(sinAsinB)=3/1#

By componendo and dividendo

#=>(cosAcosB+sinAsinB)/ (cosAcosB-sinAsinB)= (3+1)/(3-1)#

#=>cos(A-B)/ cos(A+B)= 4/2=2#

#=>2cos(A+B)=cos(A-B)#

Proved

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