MCQ
${\tan ^{ - 1}}\left[ {\frac{{\cos x}}{{1 + \sin x}}} \right] = $
- ✓$\frac{\pi }{4} - \frac{x}{2}$
- B$\frac{\pi }{4} + \frac{x}{2}$
- C$\frac{x}{2}$
- D$\frac{\pi }{4} - x$
$ = {\tan ^{ - 1}}\left[ {\frac{{2\,\sin \,(\pi /4 - x/2)\,\cos \,(\pi /4 - x/2)}}{{2\,{{\cos }^2}\,(\pi /4 - x/2)}}} \right]$
$ = {\tan ^{ - 1}}\tan \,\left( {\frac{\pi }{4} - \frac{x}{2}} \right) = \frac{\pi }{4} - \frac{x}{2}$.
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$f\left( x \right)\left\{ \begin{array}{l}
\frac{{2{x^2}}}{a}\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,0 \le x < 1\,\,\,\\
a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,\,\,\,\,1 \le x < \sqrt 2 \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\
\frac{{2{b^2} - 4b}}{{{x^3}}}\,\,\,,\,\,\,\,\,\sqrt 2 \le x < \infty
\end{array} \right.\,\,\,\,$
is continuous in the interval $\left[ {0,\infty } \right)$ , then an ordered pair $(a, b)$ is