MCQ
$2{\sin ^{ - 1}}\frac{3}{5} + {\cos ^{ - 1}}\frac{{24}}{{25}} = $
- ✓$\frac{\pi }{2}$
- B$\frac{{2\pi }}{3}$
- C$\frac{{5\pi }}{3}$
- DNone of these
✓
Answer
Correct option: A.
$\frac{\pi }{2}$
a
(a) $2\,{\sin ^{ - 1}}\frac{3}{5} + {\cos ^{ - 1}}\frac{{24}}{{25}} = {\sin ^{ - 1}}2 \times \frac{3}{5}\sqrt {1 - \frac{9}{{25}}} + {\cos ^{ - 1}}\frac{{24}}{{25}}$
(a) $2\,{\sin ^{ - 1}}\frac{3}{5} + {\cos ^{ - 1}}\frac{{24}}{{25}} = {\sin ^{ - 1}}2 \times \frac{3}{5}\sqrt {1 - \frac{9}{{25}}} + {\cos ^{ - 1}}\frac{{24}}{{25}}$
$ = {\sin ^{ - 1}}\frac{{24}}{{25}} + {\cos ^{ - 1}}\frac{{24}}{{25}} = \frac{\pi }{2}$.
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