IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

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QUESTION 3:

The sum of alll the real values of x satisfying the given equation
where = greatest integer function is ?

The minimum and maximum values of cosx are -1 and +1 respectively. Hence for a solution to occur ,

In other words,

which gives us

and

.

=>

hence the possible values of greatest integer function of 'x' are

Case 1 :

LHS = 1 .

Substituly to see that, LHS = 1 .

The only soultion is at

Case 2 :

LHS = -1

is a solution.
So is

Case 3:
Case 4:

Similarly try out for the above cases. But they have no solution.

Hence sum of the solutions is