what is the value of cos(tan^(-1)(0))? -1 0 1 π/2

Answer:

C. 1

Explanation:

Step1: Let $\theta=\tan^{-1}(0)$

By the definition of the inverse - tangent function, $\tan\theta = 0$. The range of the inverse - tangent function $y = \tan^{-1}(x)$ is $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$. In this range, when $\tan\theta=0$, $\theta = 0$.

Step2: Calculate $\cos(\theta)$

Since $\theta = 0$ from Step 1, then $\cos(\tan^{-1}(0))=\cos(0)$. And we know that $\cos(0)=1$.