MCQ
${\sin ^{ - 1}}\frac{1}{{\sqrt 5 }} + {\cot ^{ - 1}}3 $ is equal to
- A$\frac{\pi }{6}$
- ✓$\frac{\pi }{4}$
- C$\frac{\pi }{3}$
- D$\frac{\pi }{2}$
✓
Answer
Correct option: B.
$\frac{\pi }{4}$
b
(b) ${\sin ^{ - 1}}\frac{1}{{\sqrt 5 }} + {\cot ^{ - 1}}3 = {\cot ^{ - 1}}\left( {\frac{{\sqrt {1 - \frac{1}{5}} }}{{\frac{1}{{\sqrt 5 }}}}} \right) + {\cot ^{ - 1}}3$
(b) ${\sin ^{ - 1}}\frac{1}{{\sqrt 5 }} + {\cot ^{ - 1}}3 = {\cot ^{ - 1}}\left( {\frac{{\sqrt {1 - \frac{1}{5}} }}{{\frac{1}{{\sqrt 5 }}}}} \right) + {\cot ^{ - 1}}3$
$ = {\cot ^{ - 1}}(2) + {\cot ^{ - 1}}(3) = {\cot ^{ - 1}}\left( {\frac{{2 \times 3 - 1}}{{3 + 2}}} \right) = {\cot ^{ - 1}}(1) = \frac{\pi }{4}$.
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