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Question

Find the number of solutions for the equation cos1(cosx)=12.


A

1

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B

infinite

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C

0

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D

2

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Solution

The correct option is C

0


Here it is easily solved if we use the graph of the function in hand. The function on the LHS is,
f(x)=cos1(cosx){2nπ+x, xϵ[2nπ,(2n+1)π]2nπx, xϵ[(2n1)π,2nπ,nϵI].
The solutions for the equation will be intersection of the following functions.
y=cos1(cosx) & y=12.

We can see that the function y=cos1(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.


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