If f(x)=cos−1⁡(cot⁡x) ,x<π2a(π[x]−1) ,x≥π2,. denotes greatest integer functionThe value of a for f to be continuous at x=π2 is

If f(x)=cos−1⁡(cot⁡x) ,x

A
$\frac{π}{2 (π - 1)}$
B
$π - 1$
C
$\frac{π}{π + 1}$
D
$\frac{π}{π - 1}$

Solution:

$\begin{array}{l} f (π / 2) = a (π [\frac{π}{2}] - 1) = a (π - 1) \\ lim_{x \to π / 2 -} f (x) = lim_{x \to π / 2 -} \cos^{- 1} (\cot x) = \frac{π}{2} \\ ϕ ar (π - 1) = \frac{π}{2} \end{array}$

If $f (x) = \{\begin{cases} \cos^{- 1} (\cot x), x < \frac{π}{2} \\ a (π [x] - 1), x \geq \frac{π}{2}, [.] d e n o t e s g r e a t e s t i n t e g e r f u n c t i o n \end{cases}$
The value of $a$ for $f$ to be continuous at $x = \frac{π}{2}$ is

Solution:

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