Question

Cho cos a = -2/√5 với pi/2 < a< pi. Tính cos (a + pi/3), sin (pi/4 - a)

Answer 1

\(sin^2a=1-cos^2a=1-\dfrac{4}{5}=\dfrac{1}{5}\)

\(\Rightarrow sina=\dfrac{1}{\sqrt{5}}\left(\dfrac{\pi}{2}< a< \pi\right)\)

\(cos\left(a+\dfrac{\pi}{3}\right)=cosa.cos\dfrac{\pi}{3}-sina.sin\dfrac{\pi}{3}=-\dfrac{2}{\sqrt{5}}.\dfrac{1}{2}-\dfrac{1}{\sqrt{5}}.\dfrac{\sqrt{3}}{2}=-\dfrac{2+\sqrt{3}}{2\sqrt{5}}\)

\(sin\left(\dfrac{\pi}{4}-a\right)=sin\dfrac{\pi}{4}.cosa-cos\dfrac{\pi}{4}.sina=-\dfrac{2}{\sqrt{5}}.\dfrac{\sqrt{2}}{2}-\dfrac{1}{\sqrt{5}}.\dfrac{\sqrt{2}}{2}=-\dfrac{\sqrt{2}}{2\sqrt{5}}\)