what is the value of this number identity?
(sec 11)(sec 19) - (2 cot 71) = ?
Hello pacmanI haven't an exact answer, but a simplification of the expression, as follows:
$\displaystyle \sec11\sec19-2\cot71 = \frac{1}{\cos11\cos19}-2\frac{\cos71}{\sin71}$
$\displaystyle = \frac{1}{\cos11\cos19}-2\frac{\cos71}{\cos19}$, since $\displaystyle \sin A = \cos(90-A)$
$\displaystyle =\frac{1-2\cos71\cos11}{\cos11\cos19}$
$\displaystyle =\frac{1-(\cos82+\cos60)}{\cos11\cos19}$, using $\displaystyle 2\cos A \cos B = \cos(A+B)+\cos(A-B)$
$\displaystyle =\frac{0.5-\cos82}{\cos11\cos19}$
$\displaystyle =\frac{\sin30-\sin8}{\cos11\cos19}$
$\displaystyle =\frac{2\cos19\sin11}{\cos11\cos19}$, using $\displaystyle \sin A - \sin B = 2\cos\tfrac12(A+B)\sin\tfrac12(A-B)$
$\displaystyle =2\tan11$
I don't think you can go any further in terms of a numerical value.
Grandad