Answer:
[tex]\frac{3\pi}{2}[/tex].
Step-by-step explanation:
The given expression is
[tex]2\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)[/tex]
It can be rewritten as
[tex]2\cos^{-1}\left(-\frac{1}{\sqrt{2}}\right)[/tex]
[tex]2\left [\pi-\cos^{-1}\left(\frac{1}{\sqrt{2}}\right)\right][/tex] [tex][\because \cos^{-1}(-x)=\pi-\cos^{-1}(x), x\in [-1,1]][/tex]
[tex]2\left [\pi-\cos^{-1}\left(\cos \frac{\pi}{4}\right)\right][/tex]
[tex]2\left [\pi-\frac{\pi}{4}\right][/tex]
[tex]2\left [\frac{4\pi-\pi}{4}\right][/tex]
[tex]\frac{3\pi}{2}[/tex]
Hence, the exact value of given expression is [tex]\frac{3\pi}{2}[/tex].
Answer:
the choices are:
pi/3
pi/6
pi/4
pi/2
the answer is:
pi/4
Step-by-step explanation:
