Finding the exact value of $\tan(\cos^{-1} x)$ 
Find the exact values of:
    a) $\tan(\cos^{-1} x)$
    b) $\cos(\tan^{-1} x)$
    c) $\sec(\sin^{-1} x)$

My work is the following.
a) $\tan x = \sin x / \cos x$ so
$$\tan(\cos^{-1} x) = \sin(\cos^{-1} x) / \cos(\cos^{-1} x) = \sin(\cos^{-1}x) / x$$
b) $\cos(\tan^{-1} x) = \cos(\sin^{-1} x / \cos^{-1} x)$
c) $\sec(\sin^{-1} x)= 1/\cos(\sin^{-1} x)$
Is my answer correct?

Useful things to note
$$
\tan^2 x + 1 = \sec^2 x \implies \tan x = \pm\sqrt{\frac{1}{\cos^2 x}-1}
$$
And
$$
\cos^2 x+\sin^2 x = 1\implies \cos x =\pm\sqrt{1-\sin^2 x}
$$
Can you use these to your advantage?
