Question

Find the value of Sec square tan inverse 2

Answer 1

Answer:

Step-by-step explanation:

e4edf59ece7aa93a2ecda3d747bfa7b5.docx

Answer 2

Question: Find the value of $sec^2(tan^{-1}(2))$.

Answer:

The value of $sec^2(tan^{-1}(2))$ is 5.

Step-by-step explanation:

To find:-

The value of the function $sec^2(tan^{-1}(2))$.

Step 1 of 1

Consider the given trigonometric function as follows:

$sec^2(tan^{-1}(2))$ _____ (1)

Now, let $\theta=tan^{-1}(2)$.

Then,

tan$\theta$ = 2

So, consider the right triangle ABC such that ∠C = $\theta$.

As we know,

tan$\theta$ = perpendicular/base

    2 = AB/BC

⇒ AB = 2 and BC = 1

Using the Pythagoras theorem,

$AC=\sqrt{AB^2+BC^2}$

$AC=\sqrt{2^2+1^2}$

$AC = \sqrt{4+1}$

AC = $\sqrt{5}$

So,

sec$\theta$ = AC/BC

       = $\sqrt{5}/1$

sec$\theta$ = $\sqrt{5}$

From (1), we have

$sec^2\theta$ (Since $\theta=tan^{-1}(2)$)

On substituting the value of sec$\theta$, we get

$sec^2\theta=(\sqrt{5} )^2$

$sec^2\theta=5$

Therefore, the value of $sec^2(tan^{-1}(2))$ is 5.

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