Mathematics

Problem

Let

\theta

be an acute angle such that

\tan\theta = \dfrac{7}{24}

. Work through the following tasks. a. (i) Calculate

\sin\theta

and

\cos\theta

. b. (ii) Find the numerical value of

\dfrac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta}

. c. (iii) Using the ratios obtained, compute the product

\sin\theta \cos\theta

and express it as a simplified fraction.