6 sec 2 θ tan θ = 12 tan θ

Answer 1

6sec2xtanx = 12tanx tangents cancel out, divide both sides by 6tanx to get

sec2x = 2

1/cos2x = 2

cos2x =1/2

2x = 60 degrees or pi/3 or -60 degrees or -pi/3

theta =30 degrees or pi/6 radians or -30 degrees or -pi/6

+ 2npi where n= any integer

Unless you might have meant the problem to be

6sec^2xtanx = 12tanx

then

sec^2x = 2

1/cos^2x = 2

cos^2x = 1/2

cosx = + or - 1/sqr2

x = 45 degrees or pi/4 or -45 degrees or -pi/4

+ 2npi where n= any integer