Q. 5 B5.0( 1 Vote )

Solve the following equations :

tan x + tan 2x = tan 3x

Answer :


Ideas required to solve the problem:


The general solution of any trigonometric equation is given as –


• sin x = sin y, implies x = nπ + (– 1)ny, where n Z.


• cos x = cos y, implies x = 2nπ ± y, where n Z.


• tan x = tan y, implies x = nπ + y, where n Z.


given,


tan x + tan 2x - tan 3x = 0


In order to solve the equation we need to reduce the equation into factor form so that we can equate the ratios with 0 and can solve the equation easily


As if we expand tan 3x = tan ( x + 2x) we will get tan x + tan 2x common.


tan x + tan 2x - tan 3x = 0


tan x + tan 2x - tan (x + 2x) = 0


As, tan (A + B) =


tan x + tan 2x -




tan x + tan 2x = 0 or – tan x tan 2x = 0


Using, tan 2x = we have,


tan x = tan (-2x) or


tan x = tan(-2x) or tan x = 0 = tan 0


if tan x = tan y, implies x = nπ + y, where n Z


x = nπ + (-2x) or x = mπ + 0


3x = nπ or x = mπ


….ans


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