Question

Which of the following function is discontinuous at $x=a$

• A. $\tan (x-a)$
• B. $\sin (x-a)$
• C. $cosec(x-a)$
• D. $\sec (x-a)$

Answer 1

The correct option is C $cosec(x-a)$

${lim}_{x\to {\alpha }^{+}}cosec(x-a)=cosec0=+\infty$ ($x\to a^{+};(x-a)\to 0^{+}$)

${lim}_{x\to a^{-}}cosec(x-a)=-cosec0=-\infty$ ($x\to a^{-};(x-a)\to 0^{-}$)

$cosec\theta <0$ for $\theta <0$

$cosec\theta >0$ for $\theta >0$

LHL$\ne$RHL

$\therefore$ Discontinuous.