Finding the numerical value of $(1-\cot 37^\circ)(1-\cot 8^\circ)$ I found this question from an old math questionnaire.

Find the numerical value of $$(1-\cot 37^\circ)(1-\cot 8^\circ)$$

I have tried converting cotangent into cosine/sine but then I realized that I really do not know what to do. Honestly, I really do not know what to do or how to even start. Can anyone help?
 A: $$(1-\cot 37^\circ)(1-\cot 8^\circ)=(1-\cot (45-8)^\circ)(1-\cot 8^\circ) = \left(1-{1+\cot8^\circ \over\cot8^\circ-1 }\right)(1-\cot 8^\circ)=  -\left(\cot8^\circ-1-1-\cot8^\circ \right)=2$$ 
A: Hint: Prove, if you do not already know, the cotangent addition law:

$$\cot(a+b) = \frac{\cot a\cot b - 1}{\cot a + \cot b}$$

Notice that $\cot(37^{\circ}+8^{\circ}) = 1$. Now expand the expression you want to evaluate, and notice that some terms cancel very nicely.
A: $$\cot(38^\circ+7^\circ)=\frac{(\cot 37^\circ\cot 8^\circ-1)}{\cot 37^\circ+\cot 8^\circ}=\cot(45^\circ)=1$$
$$\cot 37^\circ\cot 8^\circ-\cot 37^\circ-\cot 8^\circ=1$$
$$1+\cot 37^\circ\cot 8^\circ-\cot 37^\circ-\cot 8^\circ=2$$
$$\cot 37^\circ(\cot 8^\circ-1)-(\cot 8^\circ-1)=2$$
$$(\cot 8^\circ-1)(\cot 37^\circ-1)=(1-\cot 8^\circ)(1-\cot 37^\circ)=2$$
A: Here,
$$(1-\cot 37°)(1-\cot 8°)$$
$$(1-\cot 37°)(1-\cot (45-37))$$
$$(1-\cot 37°)(1-\frac {\cot 45. \cot 37+1}{\cot 37° -\cot 45°})$$
$$(1-\cot 37°)(1-\frac {\cot 37° +1}{\cot 37° -1})$$
$$(1-\cot 37°)\times \frac {2}{1-\cot 37°}$$
$$2$$..
