$={\tan ^{ - 1}}\left( {\frac{1}{2}} \right) = \frac{1}{2}.2{\tan ^{ - 1}}\left( {\frac{1}{2}} \right) = \frac{1}{2}{\tan ^{ - 1}}\frac{{2(1/2)}}{{1 - (1/4)}}$
$ = \frac{1}{2}{\tan ^{ - 1}}\frac{4}{3} = \frac{1}{2}{\cos ^{ - 1}}\frac{3}{5}$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$\text{a}=1,\text{ b}=-1$
$\text{a}=-1,\text{ b}=1+\sqrt{2}$
$\text{a}=-1,\text{ b}=1$
$\text{None os these}.$
$a x+2 y=\lambda$
$3 x-2 y=\mu$Which of the following statement($s$) is(are) correct?
($A$) If $a=-3$, then the system has infinitely many solutions for all values of $\lambda$ and $\mu$
($B$) If $a \neq-3$, then the system has a unique solution for all values of $\lambda$ and $\mu$
($C$) If $\lambda+\mu=0$, then the system has infinitely many solutions for $a=-3$
($D$) If $\lambda+\mu \neq 0$, then the system has no solution for $a=-3$