Question

${\cos }^{-1}\left\{\frac{1}{\sqrt{2}}\left(\cos \frac{9\pi }{10}-\sin \frac{9\pi }{10}\right)\right\}=$

• A. $\frac{23\pi }{20}$
• B. $\frac{7\pi }{10}$
• C. $\frac{7\pi }{20}$
• D. $\frac{17\pi }{20}$

Answer 1

The correct option is A $\frac{23\pi }{20}$

${\cos }^{-1}\left\{\frac{1}{\sqrt{2}}(\cos \frac{9\pi }{10}-\sin \frac{9\pi }{10})\right\}$

$={\cos }^{-1}\left\{(\frac{1}{\sqrt{2}}\cos \frac{9\pi }{10}-\frac{1}{\sqrt{2}}\sin \frac{9\pi }{10})\right\}$

$={\cos }^{-1}\left\{\cos (\frac{\pi }{4}+\frac{9\pi }{10})\right\}$

$={\cos }^{-1}\left\{\cos \left(\frac{23\pi }{20}\right)\right\}$

$=\frac{23\pi }{20}$