True or false, with reason: (a) … (b) … has no solution…

True or false, with reason:
(a) $({\sin }^{-1}y{)}^2+({\cos }^{-1}y{)}^2=1$
(b) ${\sin }^{-1}y={\cos }^{-1}y$ has no solution
(c) ${\sin }^{-1}y$ is an increasing function
(d) ${\sin }^{-1}y$ is an odd function
(e) ${\sin }^{-1}y$ and $-{\cos }^{-1}y$ have the same slope—so they are the same.
(f) $\sin (\cos x)=\cos (\sin x)$

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §4.4 Inverses of Trigonometric Functions, #15