KCET 2025 Math Paper

The function given is f(x)=tan‌x−x.
To determine whether this function is increasing, decreasing, or neither, we need to analyze its derivative:
f′(x)= sec2x−1=tan2x
Since tan2x is always greater than or equal to zero (tan2x≥0), the derivative f′(x) is non-negative across its domain. This implies that the function f(x) is always increasing or at the very least, nondecreasing.
Thus, the function f(x)=tan‌x−x consistently increases.