I can't figure out the answer to this problem
Tan(sec¯¹ [sq rt.x² + 4/x])
To solve this problem, let's break it down step by step:
Step 1: Start by simplifying the innermost part of the expression.
Inside the square root, we have x² + 4/x. We can simplify this by finding a common denominator. So, for x in the denominator, we can rewrite 4/x as 4x^-1 (using the exponent property). Now we can combine the two terms:
x² + 4/x = x² + 4x^-1
Step 2: Next, we need to simplify the expression inside the inverse secant function, [sq rt.x² + 4/x].
Since the square root and inverse secant function are independent of each other, we can simplify them separately. Let's simplify the square root first:
[sq rt.x² + 4/x] = √(x² + 4x^-1)
Step 3: Now we have simplified the expression inside the inverse secant function. Next, we need to find the inverse secant of this expression.
The inverse secant function is denoted as sec¯¹, which is the inverse of the secant function. Since we have simplified the expression inside the inverse secant, we can now find its inverse secant value:
sec¯¹ √(x² + 4x^-1)
Step 4: Finally, we have the inverse secant value. The last step is to take the tangent of this inverse secant value.
Tan(sec¯¹ √(x² + 4/x))
That's the final expression. Keep in mind that the answer may further simplify based on the given value of x.