Given: A function
[tex]f(x)=\frac{1}{2}\cos2x-1[/tex]
Required: Zeroes of the function in the interval [0,2π]
Explanation:
For zero of the function f(x)
[tex]\begin{gathered} f(x)=0 \\ \frac{1}{2}\cos2x-1=0 \end{gathered}[/tex]
Now,
[tex]\begin{gathered} \frac{1}{2}\cos2x=1 \\ \cos2x=2 \end{gathered}[/tex]
Now, cos function alsways lies between [-1,1].
It is not equal to 2 in the interval [0,2π].
Hence, the zeroes does not exist in this interval.
Final Answer: The correct answer is option 1.
