Mathematics

Problem

Answer the following questions related to complementary angles: a. (i) State the relationship between

\sin(90^{\circ}-A)

and

\cos A

as well as between

\cos(90^{\circ}-A)

and

\sin A

for an acute angle

A

in a right-angled triangle. b. (ii) With the help of a labelled right-angled triangle, explain why

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

. c. (iii) Taking

A=30^{\circ}

, verify numerically that the identity stated in part (i) is true.