If α,β,γand δare the solution of the equation $$tan$$θ$$+$$π$$4=3$$ $$tan3$$θ, no two of which have equal tangents then the value of $$tan$$α$$+$$$$tan$$β$$+$$$$tan$$γ$$+$$$$tan$$δ$$=$$

Question

If α,β,γand δare the solution of the equation $$tan$$θ$$+$$π$$4=3$$ $$tan3$$θ, no two of which have equal tangents then the value of $$tan$$α$$+$$$$tan$$β$$+$$$$tan$$γ$$+$$$$tan$$δ$$=$$

Infinity Learn · Accepted Answer

If α,β,γ and δare the solutions of the equation $$tan$$θ$$+$$π$$4=3tan3$$θ⇒$$1+$$$$tan$$θ$$1$$−$$tan$$θ$$=3$$×$$3tan$$θ−$$tan3$$θ$$1$$−$$3$$ $$tan2$$θ⇒$$1+t1$$−$$t=33t$$−$$t31$$−$$3t2$$    (putting$$ $$t=$$$$tan$$θ$$)⇒$$3t4$$−$$6t2+8t$$−$$1=0$$∴sum of roots $$=$$ $$t1+t2+t3+t4=0$$⇒$$tan$$α$$+$$$$tan$$β$$+$$$$tan$$γ$$+$$$$tan$$δ$$=0$$

If $α, β, γ$ and $δ$ are the solution of the equation $\tan (θ + \frac{π}{4}) = 3 \tan 3 θ$ , no two of which have equal tangents then the value of
$\tan α + \tan β + \tan γ + \tan δ =$

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If α,β,γand δare the solution of the equation tanθ+π4=3 tan3θ, no two of which have equal tangents then the value of tanα+tanβ+tanγ+tanδ=

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If $α, β, γ$ and $δ$ are the solution of the equation $\tan (θ + \frac{π}{4}) = 3 \tan 3 θ$ , no two of which have equal tangents then the value of
$\tan α + \tan β + \tan γ + \tan δ =$