Question

if tan theta =5,where theta is an acute angle ,find sec theta using the identity

Answer 1

The value of sec$\alpha$ is given by

$\sec\alpha = \sqrt{26}$

• We have

       tan$\alpha$ = 5 , where $\alpha$ is an acute angle

       therefore

       ${tan}^{2} \alpha \: = 25$

• Now, using the identity

        ${tan}^{2} \alpha + 1 = {sec}^{2} \alpha \:$

• therefore,

         

$\sec⊖ = ± \: \sqrt{26}$

Answer 2

$\sec\theta=\sqrt{26}$

Step-by-step explanation:

We have,

$\tan \theta =5$, where, $\theta$ is an acute angle

To find, the value of $\sec \theta=?$

We know that, trigonometric identity

$\sec^2 \theta-\tan^2 \theta=1$

⇒ $\sec^2 \theta=1+\tan^2 \theta$

⇒ $\sec\theta=\sqrt{1+\tan^2 \theta}$

∴ $\sec\theta=\sqrt{1+5^2}$

$=\sqrt{1+25}=\sqrt{26}$ (since, first quadrant only + sign)

∴ $\sec\theta=\sqrt{26}$

Thus, $\sec\theta=\sqrt{26}$