Find the exact value of the expression, if it is defined. $\tan \left( \cos ^ { - 1 } ( \sqrt { 2 } / 2 ) \right]$
A)1/2
B)-1/2
C)45
D)1
E)none of these

Question

Quizplus · Accepted Answer

The expression $\cos^{-1}(\sqrt{2}/2)$ gives the angle whose cosine is $\sqrt{2}/2$. This angle is $45^\circ$ or $\pi/4$ radians. The tangent of $45^\circ$ or $\pi/4$ is 1. Therefore, the correct answer is D) 1.

Find the Exact Value of the Expression, If It Is tan⁡(cos⁡−1(2/2)]\tan \left( \cos ^ { - 1 } ( \sqrt { 2 } / 2 ) \right]tan(cos−1(2​/2)]

Find the Exact Value of the Expression, If It Is $\tan \left( \cos ^ { - 1 } ( \sqrt { 2 } / 2 ) \right]$