Question

Show that -1 < tanhx < 1 for all x

Answer 1

See....
We know Tan 45=1
When The Value of x is below45 the Value Goes within Decimal Values....

But it never Reaches Zero(Though Its Not absolute... But it dosent Goes beyond 0.

And When x increases above 45 The Value again goes Decimal... √3,... So...

Either way Its Decimal And The Highest no: is 1.

Now Let h be any Value.

so....

Tanhx will be greater than -1 and Less than 0 For When h is negative...(in certain cases atleast)

and Tanxh will be greater than 0 and less than 1 when h is positive.

so -1<tan(hx)<+1