Notes: What is tan(x-pi)?

Friday, May 15, 2015

We'll have to use the following identity to compute tan(x
- $\displaystyle\pi$ ).

$\displaystyle{\tan{{\left({a}-{b}\right)}}}$ = $\displaystyle\frac{{{\tan{{a}}}-{\tan{{b}}}}}{{{1}+{\tan{{a}}}\cdot{\tan{}}}}$
b)

We'll replace a and b by x and $\displaystyle\pi$ , such
as:

$\displaystyle{\tan{{\left({x}-\pi\right)}}}$ = $\displaystyle\frac{{{\tan{{x}}}-{\tan{\pi}}}}{{{1}+{\tan{{x}}}\cdot{\tan{}}}}$
pi)

But $\displaystyle{\tan{\pi}}=\frac{{\sin{\pi}}}{{\cos{\pi}}}=\frac{{0}}{{-{{1}}}}=$
0

$\displaystyle{\tan{{\left({x}-\pi\right)}}}=\frac{{{\tan{{x}}}-{0}}}{{{1}+{\tan{}}}}$
x*0)

$\displaystyle{\tan{{\left({x}-\pi\right)}}}={\tan{}}$
x

Therefore, the value of tangent of the
difference $\displaystyle{x}-\pi$ remains the same as the value of the tangent of the angle
x.

Notes