Write $\tan \left(\arccos (x)\right)$ as an algebraic expression in $x$.

Evaluate $\arccos \left(\cos \left(\frac{5\pi }{4}\right)\right)$.

Evaluate $\arccos \left(\cos \left(\frac{7\pi }{4}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{12}{13}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{20}{29}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{8}{17}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{24}{25}\right)\right)$.

Evaluate $\cos \left(\arctan \left(\frac{5}{12}\right)\right)$.

Write $\cos \left(\arcsin (x)\right)$ as an algebraic expression in $x$.

Evaluate $\cos \left(\arctan \left(\frac{40}{9}\right)\right)$.

Evaluate $\cos \left(\arctan \left(\frac{21}{20}\right)\right)$.

Write $\sec \left(\arctan (x)\right)$ as an algebraic expression in $x$.

Evaluate $\arcsin \left(\sin \left(\frac{5\pi }{6}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{7}{25}\right)\right)$.

Evaluate $\arctan \left(\tan \left(\frac{5\pi }{6}\right)\right)$.

Evaluate $\arctan \left(\tan \left(\frac{4\pi }{3}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{15}{17}\right)\right)$.

Evaluate $\arcsin \left(\sin \left(\frac{7\pi }{4}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{4}{5}\right)\right)$.

Write $\tan \left(\arcsin (x)\right)$ as an algebraic expression in $x$.

Evaluate $\cos \left(\arctan \left(\frac{24}{7}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{12}{13}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{9}{41}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{24}{25}\right)\right)$.

Evaluate $\cos \left(\arctan \left(\frac{3}{4}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{15}{17}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{21}{29}\right)\right)$.

Write $\sin \left(\arccos (x)\right)$ as an algebraic expression in $x$.

Evaluate $\cos \left(\arctan \left(\frac{8}{15}\right)\right)$.

Evaluate $\sin \left(\arccos \left(\frac{40}{41}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{9}{41}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{40}{41}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{7}{25}\right)\right)$.

Evaluate $\arctan \left(\tan \left(\frac{5\pi }{4}\right)\right)$.

Evaluate $\cos \left(\arctan \left(\frac{20}{21}\right)\right)$.

Evaluate $\tan \left(\arcsin \left(\frac{3}{5}\right)\right)$.

Evaluate $\arctan \left(\tan \left(\frac{5\pi }{3}\right)\right)$.

Write $\sin \left(\arctan (x)\right)$ as an algebraic expression in $x$.

Write $\cos \left(\arctan (x)\right)$ as an algebraic expression in $x$.

Evaluate $\sin \left(\arccos \left(\frac{5}{13}\right)\right)$.