MCQ
$\sin \,\left[ {{{\cos }^{ - 1}}\left( {\frac{3}{5}} \right) + {{\tan }^{ - 1}}2} \right]$ =
- ✓$\frac{2}{{\sqrt 5 }}$
- B$\frac{-2}{{\sqrt 5 }}$
- C$\frac{3}{{\sqrt 5 }}$
- D$\frac{-3}{{\sqrt 5 }}$
$=\sin \left[\sin ^{-1}\left(\frac{4}{5} \sqrt{1-\frac{4}{5}}+\frac{2}{\sqrt{5}}\right)\right]$
$=\sin \left[\sin ^{-1}\left(\frac{10}{5 \sqrt{5}}\right)\right]$
$=\frac{2}{\sqrt{5}}$
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$x^{2}-\left(5+3 \sqrt{\log _{3} 5}-5 \sqrt{\log _{5} 3}\right)x+3\left(3^{\left(\log _{3} 5\right)^{\frac{1}{3}}}-5^{\left(\log _{5} 3\right)^{\frac{2}{3}}}-1\right)=0$
then the equation, whose roots are $\alpha+\frac{1}{\beta} \text { and } \beta+\frac{1}{\alpha} \text {, }$