if the angle between two vectors is a & b is @ and angle between vectors a+b and a is O
then
 

tan@=(bsinO )/(a+bcosO )

now

tan2 @=(bsinO)2/(a+bcosO)2


now

tan2@= sec2@ -1

and

sec2@ =1/cos2@





{a2 sec2O + b2 + 2absecO}

so cos2@=



{a2sec2O + b2sec2O + 2absecO}








if @ =0



b2=b2cos2O



O=0



if @ =90



a=-bcosO



if O=90


 

-b2



tan2@=                                                                                                                                    _________________





a2+b2