what is the value of cos(tan^(-1)1)?\na. 2\nb. √2\nc. 2√2\nd. √2/2\nplease select the best answer from the…

Answer:

D. $\frac{\sqrt{2}}{2}$

Explanation:

Step1: Let $\theta = \tan^{-1}1$

This means $\tan\theta=1$.

Step2: Recall the range of $\tan^{-1}x$

The range of $y = \tan^{-1}x$ is $(-\frac{\pi}{2},\frac{\pi}{2})$. In this range, when $\tan\theta = 1$, $\theta=\frac{\pi}{4}$.

Step3: Calculate $\cos(\tan^{-1}1)$

Since $\tan^{-1}1=\frac{\pi}{4}$, then $\cos(\tan^{-1}1)=\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$.