Find the exact value of the expression.
-$$\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$$
A) 2
B) $\frac { \sqrt { 2 } } { 2 }$
C) $\sqrt { 2 }$
D) 1

Question

Quizplus · Accepted Answer

The expression $\sin^{-1}\frac{\sqrt{2}}{2}$ corresponds to an angle whose sine is $\frac{\sqrt{2}}{2}$. This is true for $\frac{\pi}{4}$ or 45 degrees, where both the sine and cosine values are $\frac{\sqrt{2}}{2}$. Therefore, $\tan\left(\sin^{-1}\frac{\sqrt{2}}{2}\right) = \tan\left(\frac{\pi}{4}\right) = 1$, since tangent is sine over cosine, and in this case, they are equal, making the tangent equal to 1.

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

Find the Exact Value of the Expression $\tan \left( \sin ^ { - 1 } \frac { \sqrt { 2 } } { 2 } \right)$