A right-angled triangle has one acute angle θ. Answer the following questions based on this information.
a. (i) Define complementary angles in the context of a right-angled triangle.
b. (ii) Prove that sin(90∘−θ)=cosθ by using the definitions of the trigonometric ratios for the two acute angles of the triangle.
c. (iii) With the help of the same triangle, explain why tan(90∘−θ)=cotθ. State each step of your reasoning clearly.