Solve the system x-y=pi/6, tanx=tan2y.

giorgiana1976 | Student

We'll note the equations of the system:

 x-y=pi/6 (1)

 tanx=tan2y (2)

We'll write tan x = sin x/cos x

tan 2y = sin 2y/ cos 2y

We'll substitute tan x and tan 2y into the second equation:

sin x/cos x = sin 2y/ cos 2y

We'll cross multiply and we'll get:

sin x*cos 2y = cos x*sin 2y

We'll move all terms to one side:

sin x*cos 2y - cos x*sin 2y = 0

sin (x - 2y) = 0

x - 2y = arcsin 0

x - 2y = 0

x = 2y(3)

We'll form the system from the equations (1) and (3):

 x - y=pi/6

x = 2y

We'll substitute x by 2y in (1):

2y - y = pi/6

y = pi/6

x = 2y

x = 2pi/6

x = pi/3

The solution of the system is: (pi/3 ; pi/6).

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question