Problem

Answer the questions that follow, giving clear reasons. a. (i) Explain why

\sin(90^{\circ}-\theta)=\cos \theta

and verify this relation numerically for

\theta=30^{\circ}

. b. (ii) Using the relation in part (i), show that

\sin 30^{\circ}+\cos 60^{\circ}=1

. c. (iii) Without carrying out any calculation, state whether

\sin 45^{\circ}-\cos 45^{\circ}

is positive, negative, or zero, and justify your answer briefly.