Mathematics

Problem

Let

\theta

be an acute angle such that

\cos \theta = \dfrac{12}{13}

. Answer the following questions. a. (i) Determine the value of

\sin \theta

. b. (ii) Simplify the expression

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

so that it contains no trigonometric function of a complementary angle. c. (iii) Hence, find the numerical value of

E

for the given

\theta