MCQ
$cos^{-1}\left\{\frac{1}{\sqrt{2}}\left(cos \frac{9\pi}{10}-sin\frac{9\pi}{10}\right)\right\}=..........$
- A$\frac{3\pi}{20}$
- B$\frac{7\pi}{20}$
- ✓$\frac{17\pi}{20}$
- D$\frac{7\pi}{10}$
$Cos^{-1}\left\{\frac{1}{\sqrt{2}}\left(cos\frac{9 \pi}{10}-sin \frac{9 \pi}{10}\right)\right\}$
$=cos\frac{9 \pi}{10}\ cos \frac{\pi}{4}-\ sin \frac{9\pi}{10} \ sin \frac{\pi}{4}$
$=cos\left(\frac{9\pi}{10}+\frac{\pi}{4}\right)$
$=cos \frac{23\pi}{20}$
$=cos\left(2\pi-\frac{23\pi}{20}\right)$
$=cos \frac{17\pi}{20}$
$\therefore cos^{-1}\left(cos \frac{17\pi}{20}\right)$
$\frac{17\pi}{20}$
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