This is a problem number 7 from ISI B.Math 2007 based on an inequality related to (sin x)/x function. Try out this problem.

**Problem: An inequality related to (sin x)/x function**

Let . Prove that .

**Discussion:**

We consider the function . The first derivative of this function is In the interval the numerator is always negative as x is less than tan x.

Hence f(x) is a monotonically decreasing function in the given interval. Hence f(x) attains least value at which equals

Therefore in the given interval.

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How to use invariance in Combinatorics – ISI Entrance Problem – Video

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