Question

What is the equation of the tangent line of `f(x) =arcsin(tanx)` at `x=pi/4`?

Answer 1

The graph of y = f(x) has dead end at `x = pi/4`. The function is not differentiable at `x=pi/4`..

Explanation:

A sine could be tan x, for `|tan x|<=1`.

So, `2k pi -pi/4<=x<=2k pi+pi/4, k = 0, +-1, +-2..`

From the definition of arc sin (tan x) as the angle whose sine is tan x, f(x) is not differentiable at `x = pi/4`.

Yet, at an interior point of any straight piece of this series of broken graphs, the derivative is 1.

The given equation is the combined equation for

y = x,

`2k pi -pi/4<=x<=2k pi+pi/4, k = 0, +-1, +-2...`