Question

Prove that the function f(x)=tanx-x is always increasing

Answer 1

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Answer 2

Answer:

As per the question,

We have been given a function,

f(x) = tan x - x

To find whether the function is increasing or decreasing, we have to differentiate the given function.

Now

On differentiating with respect to x, we get

f'(x) = sec²x - 1

Since,

tan²x = sec²x - 1

Therefore,

f'(x) = tan²x

As we know square of any number is always greater than zero and always tends to increase.

∴ tan²x ≥ 0

Hence, we can say that the given function is always increasing.