Question

Show that the equation tan(45+x) = 2tan (45-x) can be written in the form tan^2x - 6tanx + 1 = 0.

Answer 1

I assume the best approach to solving this problem is to apply the sum identity of tangent.

Answer 2

and remember that the tan of 45 is just 1

Answer 3

I am going to attempt to type out the first step of the problem and you let me know if you see any problems with it. Lets solve this one together.

Answer 4

\[\frac{ 1+\tan x }{ 1-\tan x } = 2(\frac{ 1-tanx }{ 1+tanx})\]

Answer 5

Are you confused how I derived the above equation?

Answer 6

\[1+2tanx+\tan ^{2}x = 2- 4tanx + 2\tan ^{2}x\]

Answer 7

If you expand a bit future you get the above

Answer 8

If you move all the parts to one side you will be left with your above answer

Answer 9

\[-\tan ^{2}x+6tanx-1\ = 0]

Answer 10

\[-\tan ^{2}+6tanx-1 = 0\]

Answer 11

Then multiply both sides of the equation by -1

Answer 12

Any questions?

Answer 13

wow thanks. haha i actually know where i went wrong alrd. :)