1.

Solve `tan x+tan 2x+tan 3x = tan x tan 2x tan 3x, x in [0, pi]`.

Answer» We have `tan x + tan 2x +tan 3x=tan x tan 2x tan 3x`
We know that `tan A+tan B+tan C=tan A tan B tan C`.
iff `x=n pi, n in Z`.
So form given equation, we have `x+2x+3x=n pi, n in Z`
`:. x=npi//6, n in Z`
`:. x=pi//6, 2 pi//6, 3pi//6, 4pi//6, 5pi//6, 6pi//6`
or `x=pi//6, pi//3, pi//2, 2pi//3, 5pi//6, pi`
But for `x=pi//6, 5pi//6, tan 3x` is not defined.
And for `x=pi//2, tan x` is not defined.
`:. x=pi//3, 2 pi//3, pi`


Discussion

No Comment Found

Related InterviewSolutions