Complete the identity using the triangle method

(a) $\cos (\tan ^{-1} (x))$ =

(b) $\sin ( \sec ^{-1} (x))$ =

(The inverse functions are obtained by restricting $\tan$ to the domain $-\pi/2 < \theta < \pi/2$, and $\sec$ to the domain $[0,\pi/2) \cup (\pi/2,\pi]$, and inverting them on these restricted domains. Your answers should work for every $x$ where the inverse functions are defined. Take care with signs!)