Hello RAz Quote:

Originally Posted by

**RAz** The question is

If tanA=4 and tabB=3/5, and A and B are acute angles, prove that A-B=pi/4 (pi in radians, so really it's 45degrees).

My answer is:

$\displaystyle \color{red}tan(x-y)=\frac {tan4-tan \frac {3}{5}}{1 + tan4 * tan \frac {3}{5}}\color{black}

=1

\therefore tan(x-y)=1\color{red}=\frac {\pi}{4}$

I have a feeling there is more to add. My lecturer said something about 135 being a possible answer, and I was wondering why the question included "acute"; as in first quadrant?

Your general method is OK, but your use of notation is very sloppy. Say what you mean! What you mean, of course, is:$\displaystyle \tan(A-B)=\frac {\tan A-\tan B}{1 + \tan A \tan B} = \frac{4-\tfrac35}{1+4\cdot\tfrac35}= 1$

$\displaystyle \Rightarrow A-B = \frac{\pi}{4}$

I can't see where the possible angle of $\displaystyle 135^o$ might come from. $\displaystyle \tan135^o = -1$, not $\displaystyle +1$. And if $\displaystyle A$ and $\displaystyle B$ are acute with $\displaystyle \tan A > \tan B$, then $\displaystyle A>B$. So $\displaystyle A-B$ is also acute. Hence, $\displaystyle \tan(A-B) = 1\Rightarrow A-B = 45^o$.

Grandad