Question

the maximum value of sinx+tanx

Answer 1

infinity bride sin maximum value is 1 and tan maximum value is infinity but the sum of infinity and one is infinity

Answer 2

Answer:

Hence, the maximum value of the expression do not exist.

Step-by-step explanation:

We have to find the maximum value of:

$\sin x+\tan x$

We know that the the sine function takes the value between -1 and 1.

but the tangent function goes to infinity at the points like:

$\dfrac{(2n-1)\pi}{2}$ where n belongs to integers.

Since,

we have:

$\tan x=\dfrac{\sin x}{\cos x}$

and,

$\lim_{x \to \dfrac{\pi}{2}} \dfrac{\sin x}{\cos x}=\infty$

Hence similarly we can check for other values as well.

so,

$\lim_{x \to \dfrac{\pi}{2}} \sin x+\tan x=\infty$

Hence, the maximum value of the function do not exist.