# Thread: How would you solve this equation?

1. ## How would you solve this equation?

tan12 - cot78

can someone please explain the theory and method

trying to help my younger bro, any help would be appreciated

2. If it's an equation you usually have an unknown and an equal sign.
e.g. $tan(12x) = cot(78x)$ solve for x.

3. Hellom shayanbaig_3!

I'll take a guess as what you meant . . .

Evaluate: . $\tan12^o - \cot78^o$
Note that 12° and 78° are complementary angles.
That is, they are in the same right triangle.
Code:
*
/|
/ |
/  |
/12°|
/    |y
/     |
/      |
/       |
/ 78°    |
* - - - - *
x

We see that: . $\begin{array}{ccccc}\tan12^o &=& \dfrac{opp}{adj} &=& \dfrac{x}{y} \\ \\[-3mm] \cot 78^o &=& \dfrac{adj}{opp} &=&\dfrac{x}{y} \end{array}$ . . . . They are equal !

Therefore: . $\tan12^o - \cot78^o \;=\;0$