1ive taken (x-1)3
so tan-11+tan-11=pi/2
if α is the only root of the eqn x3+bx2+cx+1=0(b<c),then the vlaue of tan-1(α) + tan-1(α-1)
a)-Ï€/2
b)Ï€/2
c)0
d)none
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10 Answers
1luk guyz..
if w is the only root (plz donot interpret w as the cube root of unity ,ts jus a symbol i intend to use)
the main thing is F(w)=0, F'(w)=0 and F"(w)=0 using this we have
w3+bw2+cw+1=0....1)
3w2+2bw+c=0.......2)
6w+2b=0..............3)
with these 3 eqn.s we have w3=-1
or w=-1
hence tan'(-1)+tan'(1/-1)=-n/2 mite be a silly mistake, but the logic sits right according to me
1i liked kamalendu's method .... change of sign .. nice one :)
well then α <0
so lets say α= -p
so tan-1(-p) + cot-1(-p)
= -tan-1(p) + Î - cot-1(p)
= Î - (tan-1(p)+ cot-1(p) )
= Î - Î /2
= Î /2 .