Trigonometry Values Pi/12

$\displaystyle \sin\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle \sin\left({\pi\over 3}-{\pi\over 4}\right)$
	$\textstyle =$	$\displaystyle -\sin\left({\pi\over 4}\right)\cos\left({\pi\over 3}\right)+ \sin\left({\pi\over 3}\right)\cos\left({\pi\over 4}\right)$
	$\textstyle =$	$\displaystyle -{\textstyle{1\over 2}}\sqrt{2}({\textstyle{1\over 2}})+{\textstyle{1\over 2}}\sqrt{3}({\textstyle{1\over 2}}\sqrt{2}\,)$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}(\sqrt{6}-\sqrt{2}\,).$	(1)

$\displaystyle \cos\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle \cos\left({\pi\over 3}-{\pi \over 4}\right)$
	$\textstyle =$	$\displaystyle \cos\left({\pi\over 4}\right)\cos\left({\pi\over 3}\right)-\sin\left({\pi\over 3}\right)\sin\left({\pi\over 4}\right)$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 2}}({\textstyle{1\over 2}}\sqrt{2}\,)+{\textstyle{1\over 2}}\sqrt{3}(-{\textstyle{1\over 2}}\sqrt{2}\,)$
	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}(\sqrt{6}+\sqrt{2}).$	(2)

$\displaystyle \sin\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}(\sqrt{6}-\sqrt{2}) \approx 0.25882$	(3)
$\displaystyle \cos\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle {\textstyle{1\over 4}}(\sqrt{6}+\sqrt{2}) \approx 0.96593$	(4)
$\displaystyle \tan\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle 2-\sqrt{3} \approx 0.26795$	(5)
$\displaystyle \csc\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle \sqrt{6}+\sqrt{2} \approx 3.86370$	(6)
$\displaystyle \sec\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle \sqrt{6}-\sqrt{2} \approx 1.03528$	(7)
$\displaystyle \cot\left({\pi\over 12}\right)$	$\textstyle =$	$\displaystyle 2+\sqrt{3} \approx 3.73205.$	(8)