Question

Please help! Evaluate each of the following without using a calculator or computer. Show your work.
a. sin(arcsin(1/2) + arcos(1/2))
b. sec(arccos(-√3/2))
c. arctan(tan(3π/4))
d. tan(arctan(3π/4))

Answer 1

\[\sin\left[\sin^{-1}{1\over2}+\cos^{-1}{1\over2}\right]\\
\quad=\sin\left[{\pi\over6}+{\pi\over3}\right]=\sin\left(\pi\over2\right)=?
\]

Answer 2

give others a shot in the same way