1. Không dùng máy tính , tính giá trị biểu thức: p=cosπ/12+cos7π/12+2sin3π/8.cosπ/8 28/08/2021 Bởi Kennedy 1. Không dùng máy tính , tính giá trị biểu thức: p=cosπ/12+cos7π/12+2sin3π/8.cosπ/8
$\begin{array}{l} \cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}} + 2\sin \dfrac{{3\pi }}{8}\cos \dfrac{\pi }{8}\\ = \cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}} + 2.\dfrac{1}{2}\left( {\sin \dfrac{\pi }{4} + \sin \dfrac{\pi }{2}} \right)\\ = \left( {\cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}}} \right) + \left( {\sin \dfrac{\pi }{4} + \sin \dfrac{\pi }{2}} \right)\\ = 2\cos \dfrac{\pi }{3}\cos \dfrac{\pi }{4} + \dfrac{{\sqrt 2 }}{2} + 1\\ = 2.\dfrac{1}{2}.\dfrac{{\sqrt 2 }}{2} + \dfrac{{\sqrt 2 }}{2} + 1\\ = \sqrt 2 + 1 \end{array}$ Bình luận
$\cos\dfrac{\pi}{12}+\cos\dfrac{7\pi}{12}+2\sin\dfrac{3\pi}{8}.\cos\dfrac{\pi}{8}$ $=2\cos\dfrac{\pi}{3}\cos\dfrac{-\pi}{4}+2.\dfrac{1}{2}\Big(\sin\dfrac{\pi}{2}+\sin\dfrac{\pi}{4}\Big)$ $=2\cos\dfrac{\pi}{3}\cos\dfrac{\pi}{4}+\sin\dfrac{\pi}{2}+\sin\dfrac{\pi}{4}$ $=2.\dfrac{1}{2}.\dfrac{\sqrt2}{2}+1+\dfrac{\sqrt2}{2}$ $=1+\sqrt2$ Bình luận
$\begin{array}{l} \cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}} + 2\sin \dfrac{{3\pi }}{8}\cos \dfrac{\pi }{8}\\ = \cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}} + 2.\dfrac{1}{2}\left( {\sin \dfrac{\pi }{4} + \sin \dfrac{\pi }{2}} \right)\\ = \left( {\cos \dfrac{\pi }{{12}} + \cos \dfrac{{7\pi }}{{12}}} \right) + \left( {\sin \dfrac{\pi }{4} + \sin \dfrac{\pi }{2}} \right)\\ = 2\cos \dfrac{\pi }{3}\cos \dfrac{\pi }{4} + \dfrac{{\sqrt 2 }}{2} + 1\\ = 2.\dfrac{1}{2}.\dfrac{{\sqrt 2 }}{2} + \dfrac{{\sqrt 2 }}{2} + 1\\ = \sqrt 2 + 1 \end{array}$
$\cos\dfrac{\pi}{12}+\cos\dfrac{7\pi}{12}+2\sin\dfrac{3\pi}{8}.\cos\dfrac{\pi}{8}$
$=2\cos\dfrac{\pi}{3}\cos\dfrac{-\pi}{4}+2.\dfrac{1}{2}\Big(\sin\dfrac{\pi}{2}+\sin\dfrac{\pi}{4}\Big)$
$=2\cos\dfrac{\pi}{3}\cos\dfrac{\pi}{4}+\sin\dfrac{\pi}{2}+\sin\dfrac{\pi}{4}$
$=2.\dfrac{1}{2}.\dfrac{\sqrt2}{2}+1+\dfrac{\sqrt2}{2}$
$=1+\sqrt2$