Let $f:[0, \pi] \rightarrow R$ be defined as $f(x)=\left\{\begin{array}{ll}\sin x, & \text { if } x \text { is irrational and } x \in[0, \pi] \\ \tan ^{2} x, & \text { if } x \text { is rational and } x \in[0, \pi]\end{array}\right\}$ The number of points in $[0, \pi]$ at which the function $f$ is continuous is :

• A

  6
• Correct answer
  B

  4
• C

  2
• D

  0

Solution

$\sin x=\tan ^{2} x$ $\sin ^{2} x=\sin x\left(1-\sin ^{2} x\right)$ $\sin x\left(\sin ^{2} x+\sin -1\right)=0$ $\sin x=0 \quad \sin x=\frac{\sqrt{5}-1}{2}$ $x=0, \pi \quad \sin ^{-1} \frac{\sqrt{5}-1}{2}, \pi-\sin ^{-1} \frac{\sqrt{5}-1}{2}$

Hence, the correct answer is option: 'B'.