Answer:
Option C
Explanation:
Plan
(i) Using definition of f(x)= cos−1(x) . we trace the curve f(x)=cos−1(cosx)
(ii) The number of solutions of an equation involving trigonometric functions and algebraic function. algebraic and algebraic functions are found using graphs of the curves
We know , cos−1(cosx) = {xifx∈[0,π]2π−xifx∈[π,2π]−2π+xifx∈[2π,3π]4π−xifx∈[3π,4π]
From above figure. it is clear that y=10−x10 and y=cos−1(cosx) intersect at three distinct points, so number of solution is 3.