Final answer:
To draw cosec and 2cosec4x and find the range of values for which y=k has no solutions, we need to plot the values of 1/sin x, multiply the reciprocal of sin(4x) by 2, and solve the equation 2cosec(4x) = k for x.
Step-by-step explanation:
The question asks to draw cosec 2cosec4x and then find the range of values for which y=k has no solutions.
First, let's define cosec as the reciprocal of sin, so cosec x = 1/sin x.
To draw cosec, we need to plot the values of 1/sin x for different values of x.
Next, we need to find the value of 2cosec4x, which means we need to multiply the reciprocal of sin(4x) by 2.
Now, to find the range of values for which y=k has no solutions, we need to find the values of x that make y=k impossible.
We can do this by solving the equation 2cosec(4x) = k for x. If there are no solutions for x, then there are no values in the range for which y=k has a solution.