Question

The value of ${\cos }^{-1}\cos \frac{5\pi }{4}$

• A. $-\frac{\pi }{4}$
• B. $\frac{\pi }{4}$
• C. $-\frac{3\pi }{4}$
• D. $\frac{3\pi }{4}$

Answer 1

The correct option is D $\frac{3\pi }{4}$

Now,

${\cos }^{-1}\cos \frac{5\pi }{4}$

$={\cos }^{-1}\cos (\pi +\frac{\pi }{4})$

$={\cos }^{-1}(-\cos \frac{\pi }{4})$

$=\pi -{\cos }^{-1}\left(\cos \frac{\pi }{4}\right)$ [ Since ${\cos }^{-1}(-x)=\pi -{\cos }^{-1}x$ ]

$=\pi -\frac{\pi }{4}$

$=\frac{3\pi }{4}$.