In the interval `[0,pi//2]`, the equation `cos^(2)x-cosx-x=0` has

Options

A. no solution
B. exactly one solution
C. exactly two solutions
D. more than two solutions

Answer

B

Explanation

Consider the curves `y=cos^(2)x cos x` and y=x.
The number of solutions of this equation is same as the number of points where these two curves intersect. We observe that `y=cos^(2)-cosx` is a continous curve in `[0,pi//2]` and remains below x-axis whereas y=x remains above x-asis. These two curves cut at (0,0). Hence, the equation `cos^(2)x -cosx=x` has exactly one solution in `[0,pi//2]`.