Write the number of points of intersection of the curves 2y
Question:

Write the number of points of intersection of the curves $2 y=-1$ and $y=\operatorname{cosec} x$.

Solution:

Given;

$2 y=-1$ and $y=\operatorname{cosec} x$

Now,

$2 y=-1 \Rightarrow y=-\frac{1}{2}$

Also,

$\operatorname{cosec} x=y$

$\Rightarrow \operatorname{cosec} x=-\frac{1}{2}$

$\Rightarrow \frac{1}{\sin x}=-\frac{1}{2}$

$\Rightarrow \sin x=-2$

The value of sine function lies between $-1$ and 1 . Therefore, the two curves will not intersect at any point.

Hence, the number of points of intersection of the curves is $0 .$

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