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Show that tan 3x tan 2x tan x = tan 3x...

Show that
`tan 3x tan 2x tan x = tan 3x - tan 2x - tan x`

Text Solution

Verified by Experts

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`
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