show that the equation can be expressed as tanx=3

Question

Sinx+cosx=2 (sinx-cosx)

Answer 1

OK since sinx/cosx = tanx, we could start by dividing everything by cosx

 

This gives

 

Sinx/cosx + cosx/cosx = 2sinx/cosx - 2cosx/cosx

 

And simplifying gives:

 

Tanx + 1 = 2 tanx - 2

 

-tanx                       +2

 

3 = tanx