inverse tan x = inverse cos 4/5

inverse cos 4/5

= cos^-1 (4/5)
= .6435..
then tan^-1 x = .6435...
x = tan .6435...
= .75

or, make a diagram with sides 3-4-5
then, if tan^-1 x = cos^-1 (4/5)
then x = tan (cos^-1(4/5) )
= 3/4 or .75

To find the value of x in the equation inverse tan(x) = inverse cos(4/5), we can use the properties of inverse trigonometric functions.

First, let's start by expressing the equation in terms of trigonometric functions rather than inverse trigonometric functions:

tan^(-1)(x) = cos^(-1)(4/5)

Now, let's use the definition of inverse trigonometric functions to rewrite the equation in terms of the original trigonometric functions:

tan[tan^(-1)(x)] = cos[cos^(-1)(4/5)]

The tangent of the inverse tangent of a value is simply the value itself, and the cosine of the inverse cosine of a value is also the value itself. Rewriting the equation using these simplifications:

x = 4/5

Therefore, the value of x in the given equation is x = 4/5.