Find the exact value of $\tan \left( \cos ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$ .
A)1
B) $\sqrt { 3 }$
C) $\sqrt { 2 }$
D) $\frac { \sqrt { 2 } } { 2 }$
E)0
F) $\frac { \pi } { 4 }$
G) $\frac { \pi } { 3 }$
H) $\frac { \pi } { 6 }$

Question

Find the exact value of $\tan \left( \cos ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$ .
A)1
B) $\sqrt { 3 }$ 
C) $\sqrt { 2 }$
D) $\frac { \sqrt { 2 } } { 2 }$
E)0
F) $\frac { \pi } { 4 }$ 
G) $\frac { \pi } { 3 }$
H) $\frac { \pi } { 6 }$

Quizplus · Accepted Answer

$\cos^{-1}\left(\frac{\sqrt{2}}{2}\right)$ corresponds to an angle whose cosine is $\frac{\sqrt{2}}{2}$. This is the angle $45^\circ$ or $\frac{\pi}{4}$ radians. The tangent of $45^\circ$ or $\frac{\pi}{4}$ is 1.

Find the Exact Value Of tan⁡(cos⁡−122)\tan \left( \cos ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)tan(cos−122​​)

Find the Exact Value Of $\tan \left( \cos ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$