Simplify the expression √x2 +1 as much as possible after substituting tan(θ) for x.

Sure, here's an attempt at simplifying the expression. By substituting tan(θ) for x, we can rewrite the expression as √(tan(θ))^2 + 1.

Now, as we know that (tan(θ))^2 + 1 = sec^2(θ), we can simplify the expression to √sec^2(θ).

But wait, there's more! The square root of a square yields the absolute value of the value inside. Therefore, we can simplify the expression further to |sec(θ)|.

So, after substituting tan(θ) for x, the expression √x^2 + 1 can be simplified to |sec(θ)|. It's as simple as that!

To simplify the expression √x^2 + 1 after substituting tan(θ) for x, we can rewrite it as √tan^2(θ) + 1.

Since tan^2(θ) + 1 = sec^2(θ), we can simplify the expression to √sec^2(θ).

Taking the square root of sec^2(θ) will yield sec(θ).

Therefore, the simplified expression is sec(θ).

To simplify the expression √(x^2 + 1) after substituting tan(θ) for x, we can follow these steps:

Step 1: Start with the expression √(x^2 + 1).

Step 2: Substitute x with tan(θ): √((tan(θ))^2 + 1).

Step 3: Simplify the expression inside the square root: √(tan^2(θ) + 1).

Step 4: Recall the trigonometric identity that states tan^2(θ) + 1 = sec^2(θ).

Step 5: Replace tan^2(θ) + 1 with sec^2(θ) in the expression: √sec^2(θ).

Step 6: Take the square root of sec^2(θ). Since the square root of a square is the absolute value of the square, we have: |sec(θ)|.

Therefore, after substituting tan(θ) for x, the simplified expression is |sec(θ)|.

I will assume you meant to type

√(x^2 + 1)

sub in tanØ we get
√(tan^2 Ø + 1)
= √sec^2 Ø
= sec Ø