# Math Help - number identity

1. ## number identity

what is the value of this number identity?

(sec 11)(sec 19) - (2 cot 71) = ?

3. Matt, it is degrees. I am too lazy to learn LATEX. Sorry for the mishap . . . .

i wonder what trigonometric identity generated this strange number.

4. Hello pacman
Originally Posted by pacman
what is the value of this number identity?

(sec 11)(sec 19) - (2 cot 71) = ?
I haven't an exact answer, but a simplification of the expression, as follows:

$\sec11\sec19-2\cot71 = \frac{1}{\cos11\cos19}-2\frac{\cos71}{\sin71}$

$= \frac{1}{\cos11\cos19}-2\frac{\cos71}{\cos19}$, since $\sin A = \cos(90-A)$

$=\frac{1-2\cos71\cos11}{\cos11\cos19}$

$=\frac{1-(\cos82+\cos60)}{\cos11\cos19}$, using $2\cos A \cos B = \cos(A+B)+\cos(A-B)$

$=\frac{0.5-\cos82}{\cos11\cos19}$

$=\frac{\sin30-\sin8}{\cos11\cos19}$

$=\frac{2\cos19\sin11}{\cos11\cos19}$, using $\sin A - \sin B = 2\cos\tfrac12(A+B)\sin\tfrac12(A-B)$

$=2\tan11$

I don't think you can go any further in terms of a numerical value.