Find the number of solutions for the equation cos−1(cosx)=−12.
0
Here it is easily solved if we use the graph of the function in hand. The function on the LHS is,
f(x)=cos−1(cosx){−2nπ+x, xϵ[2nπ,(2n+1)π]2nπ−x, xϵ[(2n−1)π,2nπ,nϵI].
The solutions for the equation will be intersection of the following functions.
y=cos−1(cosx) & y=−12.
We can see that the function y=cos−1(cosx) gives only non-negative values and hence do not intersect with the line y=−12. ∴ Number of solutions for the given equation is zero.