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Maths-

General

Easy

Question

The general solution of the trigonometric equation tan x + tan 2x + tan 3x = tan x · tan 2x tan 3x is
where n $element of$ I

x = n $π$
$n π \pm \frac{π}{3}$
x = 2n $π$
$x = \frac{n π}{3}$

The correct answer is: $x equals fraction numerator n pi over denominator 3 end fraction$

We know that
tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x
hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x
Þ tan x + tan 2x = 0
\ tan 2x = tan (– x)
2x = np – x
$x equals fraction numerator n pi over denominator 3 end fraction comma n element of I$

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