Mathematics

Problem

For an acute angle

\theta

it is given that

\sin\theta=\dfrac{3}{5}

. Answer the following. a. (i) Find the exact value of

\cos\theta

. b. (ii) Calculate the value of

\dfrac{1-\cos^{2}\theta}{\sin^{2}\theta}

. c. (iii) Using your results from parts (i) and (ii), show that the expression in part (ii) simplifies to 1.