Tính giá trị của biểu thức sau

Đáp án:

$a)A=\dfrac{\sqrt{2}}{2}\\ b)A=\dfrac{\sqrt{2}}{8}.$

Giải thích các bước giải:

$a)A=\cos^2 \dfrac{\pi}{8}-\sin^2 \dfrac{\pi}{8}\\ =\cos \left(2. \dfrac{\pi}{8}\right)\\ =\cos  \dfrac{\pi}{4}\\ =\dfrac{\sqrt{2}}{2}\\ b)A=\sin \dfrac{\pi}{16}. \cos \dfrac{\pi}{16}. \cos \dfrac{\pi}{8}\\ =\dfrac{1}{2}.\left(2.\sin \dfrac{\pi}{16}. \cos \dfrac{\pi}{16}\right). \cos \dfrac{\pi}{8}\\ =\dfrac{1}{2}.\sin\left(2. \dfrac{\pi}{16}\right). \cos \dfrac{\pi}{8}\\ =\dfrac{1}{2}\sin\dfrac{\pi}{8} \cos \dfrac{\pi}{8}\\ =\dfrac{1}{4}.2\sin\dfrac{\pi}{8} \cos \dfrac{\pi}{8}\\ =\dfrac{1}{4}.\sin \left(2. \dfrac{\pi}{8}\right)\\ =\dfrac{1}{4}\sin\dfrac{\pi}{4}\\ =\dfrac{1}{4}.\dfrac{\sqrt{2}}{2}\\ =\dfrac{\sqrt{2}}{8}.$