Solve for x tan6xtan3x 0 pi2Solutiontan6xtan3x 0 pi2 use the

Solve for x.

tan6x=tan3x [0, pi/2)

use the trig formula : tan2y = 2tany/( 1-tan^2y)

tan6x = 2tan(3x)/( 1- tan^2(3x) )

So,2tan(3x)/( 1- tan^2(3x) ) = tan3x

tan(3x) { 2/(1- tan^2(3x) -1 } =0

tan(3x) =0

3x =0, pi----> x =0, pi/3

2/(1- tan^2(3x) ) -1 =0

2 = 1- tan^2(3x)

tan^2(3x) = -1 ( no real solution) So, neglect this solution.

Solution : x = 0 , pi/3