Evaluate exactly.
-$\tan \left( \sec ^ { - 1 } 1 \right) + \cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right)$

Question

Quizplus · Accepted Answer

The expression can be evaluated step by step. First, $\sec^{-1}(1)$ is the angle whose secant is 1, which is 0 degrees or 0 radians because $\sec(0) = 1/\cos(0) = 1$. Therefore, $\tan(\sec^{-1}(1)) = \tan(0) = 0$. Next, $\tan^{-1}(-\sqrt{3})$ is the angle whose tangent is $-\sqrt{3}$, which corresponds to $-60$ degrees or $-\pi/3$ radians. Therefore, $\cos(\tan^{-1}(-\sqrt{3})) = \cos(-\pi/3) = 1/2$. Adding these results gives $0 + 1/2 = 1/2$.

Evaluate Exactly tan⁡(sec⁡−11)+cos⁡(tan⁡−1(−3))\tan \left( \sec ^ { - 1 } 1 \right) + \cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right)tan(sec−11)+cos(tan−1(−3​))

Evaluate Exactly $\tan \left( \sec ^ { - 1 } 1 \right) + \cos \left( \tan ^ { - 1 } ( - \sqrt { 3 } ) \right)$