Question

solve tan3x+tan2x+tanx=0​

Answer 1

Step-by-step explanation:

tanx + tan2x+ tan3x=0

or, tanx+ tan2x= - tan3x

or, (sinx/cosx)+(sin 2x /Cos 2x)=-(sin 3x /cos 3x)

or, (sin x *cos 2 X + cos x *sin 2x)/cos x * cos 2x = -sin 3x / cos 3x

or, sin( 2x+x)* cos 3x= - cos x *cos 2x *sin 3x

or, sin 3x*cos 3x+ cos x * cos 2x *sin 3x =0

or, sin 3x ( cos 3x + cos x *cos 2x)=0

or, sin 3x (cos ( 2x + x)+ cos x * cos 2x)=0

or, sin 3x (cos x *cos 2x - sin x *sin 2x+ cos x *cos 2x) =0

or, -sin 3x *sin x * sin 2x=0

Either sin3x=0

i.e, 3x=nπ

i.e, X=nπ/3

or, sin 2x=0

i.e, 2x=nπ

i.e, X= nπ/2

or, sin x= 0

i.e, X=nπ

Required solution is X= nπ/3.

⚡Hope it will help you.⚡